@incollection{AST_1999__258__1_0, author = {Freiman, Gregory A.}, title = {Structure theory of set addition}, booktitle = {Structure theory of set addition}, editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.}, series = {Ast\'erisque}, pages = {1--33}, publisher = {Soci\'et\'e math\'ematique de France}, number = {258}, year = {1999}, zbl = {0958.11008}, mrnumber = {1701187}, language = {en}, url = {http://www.numdam.org/item/AST_1999__258__1_0/} }
TY - CHAP AU - Freiman, Gregory A. TI - Structure theory of set addition BT - Structure theory of set addition AU - Collectif ED - Deshouilliers Jean-Marc ED - Landreau Bernard ED - Yudin Alexander A. T3 - Astérisque PY - 1999 SP - 1 EP - 33 IS - 258 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_1999__258__1_0/ LA - en ID - AST_1999__258__1_0 ER -
%0 Book Section %A Freiman, Gregory A. %T Structure theory of set addition %B Structure theory of set addition %A Collectif %E Deshouilliers Jean-Marc %E Landreau Bernard %E Yudin Alexander A. %S Astérisque %D 1999 %P 1-33 %N 258 %I Société mathématique de France %U http://www.numdam.org/item/AST_1999__258__1_0/ %G en %F AST_1999__258__1_0
Freiman, Gregory A. Structure theory of set addition, in Structure theory of set addition, Astérisque, no. 258 (1999), pp. 1-33. http://www.numdam.org/item/AST_1999__258__1_0/
[1] Independent sets in regular graphs and sum-free subsets of finite groups, Israel J. Math. 73 (1991), 247-256. | DOI | MR | Zbl
,[2] Subset sums, J. Number Theory 27 (1987), 196-205. | DOI | MR | Zbl
,[3] On sums of subsets of a set of integers, Combinatorica 8(4) (1988), 297-306. | DOI | MR | Zbl
, ,[4] Sum free subsets in "A tribute to P. Erdos", edited by A. Baker, B. Bollobas, A. Hajnal, Cambridge University Press, Cambridge, England, (1990), 13-26. | MR | Zbl
, ,[5] Sidon sets in groups and induced subgraphs of Cayley graphs, Europ. J. Comb. 6 (1985), 101-114. | DOI | MR | Zbl
, ,[6] An algorithm for large zero-one knapsak problems, Operations Research 28 (1980), 1130-1154. | DOI | MR | Zbl
, ,[7] On rings with redundancy in multiplication, Arch. Math. 51 (1988), 500-504. | DOI | MR | Zbl
, ,[8] Non-solvable groups with large fraction of involutions, this volume. | Numdam | Zbl
,[9] Questions on set squaring in groups, this volume. | Numdam | Zbl
,[10] On the connection between some numeric characteristics of a finite group and the structure of the group, (1981), manuscript.
, ,[11] Small squaring and cubing properties for finite groups, Bull. Australian Math. Soc. 44(3) (1991) 429-450. | DOI | MR | Zbl
, , ,[12] Analytical methods of discrete optimization, CEMI (1979), 89-105.
, ,[13] Sets of integers with large trigonometric sums, this volume. | Numdam | Zbl
,[14] Analyse de la loi asymptotique de la distribution des nombres premiers generalises I, Acta Math. 68 (1937), 255-291. | DOI | JFM | MR | Zbl
,[15] On the -permutational property for groups, Arch. Math. 48 (1987), 281-285. | DOI | MR | Zbl
, , ,[16] Structure of sets with small sumset, this volume, | Numdam | Zbl
,[17] Rewriting products of group elements I, J. Alg. 116 (1988), 506-521. | DOI | MR | Zbl
,[18] Rewriting products of group elements II, J. Alg. 119 (1988), 246-259. | DOI | MR | Zbl
,[19] Recent progress on rewritability in groups, in "Group Theory" (Proc. of the 1987 Singapore Conf.), de Gruyter, Berlin-New York (1989), 77-85. | DOI | MR | Zbl
, ,[20] Tight semigroups, Public. de l'lnstitute Math., 50(64) (1991), 71-84. | EuDML | MR | Zbl
, ,[21] On arithmetic progression in sums of sets of integers in "A tribute to P. Erdos", eds. A. Baker, B. Bollobas, A. Hajnal, Cambridge Univ. Press, Cambridge, England (1990), 105-109. | DOI | MR | Zbl
,[22] Set multiplication in groups, Thesis for the degree of Ph.D., Tel Aviv University, 1992.
,[23] On -special elements in groups, Comm. Algebra 20 (1992), 3301-3320. | DOI | MR | Zbl
,[24] Structure of quasi-invariant sets, Arch. Math. (Basel) 59 (1992), 322-326. | DOI | MR | Zbl
,[25] A characterization of abelian groups, Proc. Amer. Math. Soc. 117 (1993), 627-629. | DOI | MR | Zbl
,[26] Groups with small cardinality of the cubes of their two-element subsets, Ann. New York Acad. Sci. 410 (1983), 75-82. | DOI | MR | Zbl
, ,[27] On the product of finite subsets in a torsion-free group, J. of Algebra 130 (1990), 462-476. | DOI | MR | Zbl
, ,[28] On two-element subsets in group, Ann. New York Acad. Sci. 373 (1981), 183-190. | DOI | MR | Zbl
, ,[29] Special elements in groups, in "Group Theory" (Proc. 2nd Internat. Conf., Bressanone, Italy 1989), Suppl. Rend. Circ. Mat. Palermo, II series 23 (1990), 33-42. | MR | Zbl
, , ,[30] Free numerical semigroups with power densities, Dokl. Akad. Nauk SSSR (N.S.) 118 (1958), 855-857 [Russian]. | MR | Zbl
,[31] Free numerical semigroups with power densities, Mat. Sb. (N.S.) 46(88) (1958), 143-158 [Russian]. | MR
,[32] Elementary solutions of inverse problems on bases of free semigroups Mat. Sb. (N.S.) 50(92) (1960), 221-232 [Russian]. | MR
,[33] The remainder term in the asymptotic formula for , Izv. Vyss. Učebn. Zaved. Matematika 6(19) (1960), 40-49 [Russian]. | MR
,[34] On groups generated by a pair of elements with small third or fourth power, this volume, | Numdam | Zbl
,[35] Analytical methods in integer programming, Moscow, CEMI 48 (1980) [Russian]
, ,[36] Portrait of a typical sum free set, London Math. Soc. Lecture Notes Series 123(1987), 13-42 | MR | Zbl
,[37] On the number of sets of integers with various properties, in "Number Theory", Banff, Alberta 1988 conference proceedings, de Gruyter Berlin (1990), 61-79. | MR | Zbl
, ,[38] Recherches sur les nombres, J. École Polytechn. 9 (1813), 99-116.
,[39] Fast exact and approximate algorithm for -partition and scheduling independent tasks, Discrete Mathematics 114 1993, 87-103. | DOI | MR | Zbl
,[40] Solving value-independent knapsack problem with the use of methods of additive number theory, Congressus Numerantium 72 (1990), 115-123. | MR | Zbl
,[41] Subset sum problem with different summands: Computations, Discrete Applied Mathematics 27 (1990), 277-282. | DOI | MR | Zbl
,[42] New structural approach to integer programming: a survey, this volume, | Zbl
,[43] New algorithm for Dense Subset-Sum Problem, this volume, | Numdam | Zbl
,[44] Solving dense subset-sum problems by using analytic number theory, J. of Complexity, 5 (1989), 271-282. | DOI | MR | Zbl
, , ,[45] Hard knapsak problems, Operations Research 28 (1980), 1402-1411. | DOI | MR | Zbl
,[46] Intersetting codes and independent families, Telecom Paris 92C003, Oct. 1992. | Zbl
, ,[47] Subset sums and coding theory, this volume | Numdam | Zbl
, ,[48] The second pearl of the theory of numbers I, Nederl. Akad. Wetensch., Proc. 52 (1949), 696-704 | MR | Zbl
, ,The second pearl of the theory of numbers I, or Indagationes Math. 11 (1949), 226-234. | MR | Zbl
, ,[49] Su di un problema combinatorio in teoria dei gruppi, Atti. Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 74(8) (1983), 136-142. | EuDML | MR | Zbl
, , ,[50] On addition of residue sets, J. London Math. Soc. 10 (1935), 30-32. | DOI | JFM | Zbl
,[51] On an additive problem of Erdős and Straus I, Israel J. Math., 92, (1995), no. 1-3, 33-43. | DOI | MR | Zbl
, ,[52] On an additive problem of Erdős and Straus II, this volume, | Numdam | Zbl
, ,[53] On series of discrete random variables 1: Real trinomial distribution with fixed probabilities, this volume, | Numdam | Zbl
, , ,[54] On the structure of sum-free sets 2, this volume, | Numdam | Zbl
, , , ,[55] On Bounds for the Concentration Function, 1 this volume, | Numdam | Zbl
, , ,[56] On a local limit theorem, manuscript 1992.
, , ,[57] The prime number theorem for Beurling's Generalized Numbers, J. of Number Theory 1(2) (1969), 200-207. | DOI | MR | Zbl
,[58] Asymptotic distribution of Beurling's Generalized Numbers, Illinois Journal of Mathematics 14(1) (1970), 12-28. | MR | Zbl
,[59] A set of generalized numbers showing Beurling's theorem to be sharp, Illinois Journal of Mathematics 14(1) (1970), 29-34. | MR | Zbl
,[60] Chebyshev estimates for Beurling generalized prime numbers, Proc. of the American Math. Soc. 39(3) (1973), 503-508. | DOI | MR | Zbl
,[61] When do Beurling's generalized numbers have a density? J. fur die reine und angewandte Math. 259 (1977), 22-39. | EuDML | MR | Zbl
,[62] An addition theorem for abelian groups of order , Journal of Number Theory 7 (1975) 33-48. | DOI | MR | Zbl
,[63] Combinatorial problems in finite Abelian groups, in "A Survey of combinatorial Theory", eds. J. N. Srivastava et al., North Holland Publishing Company (1973), 95-100. | MR | Zbl
, ,[64] Sur les sommes d'un grand nombre des variables aleaqtoires independentes Bull. Sc. Math. 63 (1939), 23-32 and 35-64. | Zbl
,[65] A theorem on the densities of sets of integers, J. London Math. Soc. 20 (1945), 8-14. | DOI | MR | Zbl
,[66] Small Chebyshev systems made by products J. of Approximation theory, 57(3) (1989), 259-267. | DOI | MR | Zbl
,[67] On an elementary proof of some asymptotic formulas in the theory of partitions, Ann. of Math. 48(3) (1942), 437-450. | DOI | MR | Zbl
,[68] Some problems and results on combinatorical number theory, in "Graph theory and its Applications : East and West (Jinan, 1986)", Ann. New York Acad. Sci. 576 (1989), 132-145 | MR | Zbl
,[69] Some remarks on number theory III, Math. Lapok 13 (1962), 28-38. | MR | Zbl
,[70] On two additive problems, J. Number Theory, 34 (1990), 1-12. | DOI | MR | Zbl
, ,[71] Theorem in the additive number theory, Bull. Research Council Israel 10F (1961), 41-43. | MR | Zbl
, , and ,[72] On a linear diophantine problem of Frobenius, Acta Arithmetica XXI (1972), 399-408. | DOI | EuDML | MR | Zbl
, ,[73] On the addition of residue classes mod , Acta Arithmetica, 9 (1964), 149-159. | EuDML | MR | Zbl
, ,[74] Sumsets containing infinite arithmetic progressions, J. Number Theory, 28 (1988), 159-166. | DOI | MR | Zbl
, , ,[75] Sommes de sous ensembles, Sem. Th. Nb. Bord. 3 (1991), 55-72. | DOI | EuDML | Numdam | MR | Zbl
, , ,[76] Arithmetic progressions in subset sums, Discrete Math. 102(3) (1992), 249-264. | DOI | MR | Zbl
, ,[77] On the Kolmogorov-Rogosin inequality for the concentration functions, Z. Wahrscheinlichkeitstheorie und verw. Gebiete 5 (1966), 210-216. | DOI | MR | Zbl
,[78] On the representation of integers as sums of distinct terms from a fixed sequence, Canad. J. Math. 18 (1966), 643-655. | DOI | MR | Zbl
,[79] An analytical method of analysis of linear Boolean equations, Ann. N.Y. Acad. Sci. 337 (1980) 97-102. | DOI | MR | Zbl
,[80] Dense sequences in the theory of partitions, Elabuz. Gos. Ped. Inst. Ucen. Zap. 3 (1958), 120-137 [Russian]. | MR
,[81] Foundations of a structural theory of set addition", Elabuz. Gos. Ped. Inst., Kazan, 1966 [Russian]. | Zbl
, "[82] Foundations of a structural theory of set addition", Translations of Mathematical Monographs 37, Amer. Math. Soc., Providence, R.I., 1973. | MR | Zbl
, "[83] Groups and the inverse problems of the additive set theory, in "Number-theoretic investigations on the Markov spectrum and the structure theory of set addition", Kalinin Gos. Univ. Moscow 1973, 175-183 [Russian]. | MR | Zbl
,[84] Inverse problems in additive number theory, Proc. of the IV Ail-Union Math. Congr. 2 (1964), 142-146. | MR | Zbl
,[85] Inverse problems in additive number theory, Uč. Zap. Kazan Univ. 115(14) (1955), 109-115 [Russian]. | MR
,[86] Inverse problems in additive theory of numbers, Izv. Acad. Nauk. SSSR Ser. Mat. 19 (1955) 275-284 [Russian]. | MR | Zbl
,[87] The addition of finite sets I, Izv. Vyss. Učebn. Zaved. Matematika 6(13) (1959), 202-213 [Russian] | MR | Zbl
,[88] Inverse problems of the additive theory of numbers. On the addition of sets of residues with respect to a prime modulus, Dokl. Akad. Nauk SSSR 141(3) (1961), 571-573 [Russian]; Soviet Math. Dokl. 2 (1961), 1520-1522 [English translation]. | MR | Zbl
,[89] Inverse problems in additive number theory VI. On the addition of finite sets III. Addition of different sets, Izv. Vyss. Učebn. Zaved. Mathematika 3(28) (1962), 151-157 [Russian]. | MR | Zbl
,[90] Inverse problems in additive number theory VII. On the addition of finite sets IV. The method of trigonometric sums, Izv. Vyss. Učebn. Zaved. Matematika 6(31) (1962), 131-134 [Russian]. | MR | Zbl
,[91] Inverse problems in additive number theory VIII. On a conjecture of P. Erdős, Izv. Vyss. Učebn. Zaved. Matematika 3(40) (1964), 156-169 [Russian]. | MR | Zbl
,[92] Inverse problems in additive number theory IX. The addition of finite sets V, Izv. Vyss. Učebn. Zaved. Matematika 6(43) (1964), 168-178 [Russian]. | MR | Zbl
,[93] New analytical results in subset sum problem, Proc. of the French-Israeli Conference on Combinatorics and Algorithms, Jerusalem 1988, Discrete Math. 114 (1993), 205-217. | MR | Zbl
,[94] Nonclosed semigroups with cancellations, Ann. N.Y. Acad. Sci. 410 (1983), 91-98. | DOI | MR | Zbl
,[95] Number-Theoretic Studies in Markov Spectrum and in the structural theory of set addition", Kalinin Gos. Univ. Moscow 1973 [Russian]. | MR | Zbl
(Editor), "[96] On extremal additive problems of Paul Erdos, in "The Proceedings of the Second International Conference on Combinatorial Mathematics and Computing, Canberra, 1987", ARS Combinatoria 26B (1988), 93-114. | MR | Zbl
,[97] On solvability of a system of two boolean linear equations, Number theory (New York, 1991-1995), 135-150, Springer, New York, 1996. | MR | Zbl
,[98] On the addition of finite sets, Dokl. Akad. Nauk SSSR 158 (1964), 1038-1041 [Russian]. | MR | Zbl
,[99] Partitions into distinct large parts, J. Austral. Math. Soc. Ser. A 57(3) (1994), 386-416. | DOI | MR | Zbl
, ,[100] On the measure of large trigonometric sums, Ann. N.Y. Acad. Sci. 452 (1985), 363-371. | DOI | MR | Zbl
,[101] On the structure and the number of sum-free sets, Asterisque 209 (1992), 195-203. | Numdam | MR | Zbl
,[102] On two- and three-element subsets of groups, Aequationes Math. 22 (1981), 140-152. | DOI | EuDML | MR | Zbl
,[103] Subset-sum problem with different summands, Congressus Numeran-tium 70 (1990), 207-215. | MR | Zbl
,[104] Sumsets and powers of , Coll. Math. Soc. J. Bolyai 60 [Budapest] (1991), 279-286. | MR | Zbl
,[105] What is the structure of if is small?, in "Lecture Notes in Mathematics 1240", Springer-Verlag, New York 1987, 109-134. | MR | Zbl
,[106] Sumsets with distinct summands and the conjecture of Erdös'-Heilbronn on sums of residues, this volume, | Numdam | Zbl
, , ,[107] A lower estimation for the cardinality of finite difference sets, Problems of Computer Science 202 (1987), 63-73. | MR
, , ,[108] A lower estimation for the cardinality of finite difference sets in , in "Proc. Conf. Number Theory, Budapest 1987", Coll. Math. Soc. J. Bolyai 51, North-Holland and Bolyai Taursulat, Budapest 1989, 125-139 | MR | Zbl
, , ,[109] Integer sum sets containing long arithmetic progressions, J. London Math. Soc. 46(2) (1992), 193-201. | DOI | MR | Zbl
, , ,[110] The general principles of additive number theory, in "Number theory", Kalinin Gos. Univ. Moscow 1973, 135-147 [Russian]. | MR | Zbl
, ,[111] Inverse problems of additive number theory and local limit theorems for lattice random variables, in "Number Theory", Kalinin Gos. Univ. Moscow 1973, 148-162 [Russian]. | MR | Zbl
, , ,[112] Structural theory of set addition and local limit theorems for independent lattice random variables, Teor. Verojatnost. i Primen. 19 (1974), 52-62 [Russian]. | MR | Zbl
, , ,[113] The relation between the invariants and , in "Number Theory", Kalinin Gos. Univ. Moscow 1973, 172-174 [Russian]. | MR | Zbl
, ,[114] Structure theory of set addition, this volume, | Numdam | Zbl
,[115] Structure of -groups, manuscript 1995.
, , ,[116] Group and semigroup theoretic considerations inspired by inverse problems of additive number theory, in "Lecture Notes in Mathematics 1320", Springer-Verlag, New York 1988, 121-140. | MR | Zbl
, ,[117] Interconnections between the structure theory of set addition and rewritability in groups, Proc. of Amer. Math. Soc. 113(4) (1991), 899-910. | MR | Zbl
, ,[118] Structure of -groups, Israel Journal of Mathematics, 77 (1992), 17-31. | DOI | MR | Zbl
, ,[119] An almost linear-time algorithm for the dense subset-sum problem, SIAM J. Comput. 20, (1991), no. 6, 1157-1189. | DOI | MR | Zbl
, ,[120] Chebyshev systems of minimal degree, SIAM J. Math. Anal. 15 (1984), 166-169. | DOI | MR | Zbl
, ,[121] Moment spaces of minimal dimension, Journal of Approximation Theory, 49(4), (1987), 390-397. | DOI | MR | Zbl
,[122] What is the probability that two group elements commute?, Amer. Math. Monthly 80 (1973), 1031-1034. | DOI | MR | Zbl
,[123] Minkowskische Addition und Subtraktion beliebiger Punktmengen und die Theoreme von Erhard Schmidt, Math. Z. 53 (1950), 210-218. | DOI | EuDML | MR | Zbl
,[124] Sur les atomes d'un graphe orienté, C.R. Acad. Sci. Paris A 284 (1977), 1253-1256. | MR | Zbl
,[125] Quelques problèmes de connexité dans les graphes orienté, J. Comb. Theory B 30 (1981), 1-10. | DOI | MR | Zbl
,[126] An application of connectivity theory in graphes to factorizations of elements in groups, Europ. J. Comb. 2 (1981), 349-355. | DOI | MR | Zbl
,[127] On the connectivity of Cayley digraphs, Europ. J. Comb. 5 (1984), 309-312. | DOI | MR | Zbl
,[128] On a subgroup contained in words with a bounded length, Discrete Math. 103 (1992), 171-176. | DOI | MR | Zbl
,[129] Subsets with small sums in abelian groups, I., European J. Combin., 18, (1997), no. 5, 541-556. | DOI | MR | Zbl
,[130] On bases in -finite groups, Math. Scand. 78 (1996), no. 2, 246-254. | DOI | EuDML | MR | Zbl
, ,[131] Vosperian and superconnected abelian Cayley digraphs, Graphs and Combinatorics 7 (1991), 143-152. | DOI | MR | Zbl
, , ,[132] On the representation of some integers as a subset sum, Bull. London Math. Soc, 26, (1994), 557-563. | DOI | MR | Zbl
,[133] On weighted sums in abelian groups, Discrete Math., 162, (1996), 127-132. | DOI | MR | Zbl
,[134] On inverse additive problems, Report Institut Blaise Pascal, EC9501 (1995).
,[135] The representation of some integers as a subset sum, EC 94/03, preprint March 1994. | MR | Zbl
,[136] Subsets with a small product in groups, this volume.
,[137] An Isoperimetric method in Additive Theory, J. Algebra, 179, (1996), 622-630. | DOI | MR | Zbl
,[138] Integers sets containing no arithmetic progressions, J. London Math. Soc. 35(2) (1987), 385-394. | DOI | MR | Zbl
,[139] On the measure of sum-sets I, Proc. London Math. Soc. 3(3) (1953), 182-194. | MR | Zbl
, ,[140] New results on subset multiplication in groups, this volume. | Numdam | Zbl
,[141] Products of conjugacy classes in groups, Lecture notes in Mathematics 1112, Springer-Verlag, 1985. | MR | Zbl
, ,[142] On a combinatorial problem in group theory, Israel J. Math., 82, (1993), no. 1-3, 329-340. | DOI | MR | Zbl
, , ,[143] Trivial integer programs unsolvable by branch and bound, Mathematical Programming bf 6 (1974), 105-109. | DOI | MR | Zbl
,[144] Commutativity in non-Abelian groups, Ph.D. Thesis, University of California, Los-Angeles 1969. | MR
,[145] Groups with representations of bounded degree, Canad. J. Math. 1 (1949), 105-112. | DOI | MR | Zbl
,[146] On complexes in a semigroup, Indagat. Math. 18 (1956), 247-254. | DOI | MR | Zbl
,[147] On product sets in locally compact groups, Fund. Math. 56 (1964), 51-68. | DOI | EuDML | MR | Zbl
,[148] On small sumsets in an abelian group, Acta Math. 103 (1960), 63-88. | DOI | MR | Zbl
,[149] Scherk P., On sums of sets of integers, Can. J. Math. 6 (1954), 238-252. | DOI | MR | Zbl
,[150] A sharper form of the Doeblin-Levy-Kolmogorov-Rogosin inequality for concentration functions, Math. Scand. 25 (1969), 133-144. | DOI | EuDML | MR | Zbl
,[151] Three pearls of number theory", Graylock, Rochester, New York, 1952. | MR | Zbl
, in "[152] Optimum designs in regression problems, Ann. Math. Stat. 30 (1959), 271-294. | DOI | MR | Zbl
, ,[153] Abschatzung der asymptotischen Dichte von Summenmengen, Math. Zeit. 58 (1953), 459-484. | DOI | EuDML | MR | Zbl
,[154] Ein Satz uber Abelsche Gruppen mit Anwendungen auf die Geometrie der Zahlen, Math. Z. 61 (1955), 429-434. | DOI | EuDML | MR | Zbl
,[155] Summenmengen in lokalkompakten abelschen Gruppen, Math. Z. 66 (1956), 88-110. | DOI | EuDML | MR | Zbl
,[156] Sur les propriétés des fonctions de concentrations de M.P. Lévy, Ann. Inst. H. Poincaré Sect. B. 16 (1) (1958), 27-34. | EuDML | Numdam | MR | Zbl
,[157] On addition of two distinct sets of integers, Acta Arithmetica, LXX.l, (1995), 85-91. | DOI | EuDML | MR | Zbl
, ,[158] On the structure of sets of integers with small doubling property , unpublished manuscript.
,[159] On the extremal aspect of Frobenius problem, J. Comb. Th. (Series A), 73 (1), (1996), 111-119. | DOI | MR | Zbl
,[160] Representing powers of by a sum of four integers, Combinatorica, 16 (3) (1996), 413-416. | DOI | MR | Zbl
,[161] Structure theorem for multiple addition and the Frobenius problem, Journal of Number Theory, 58 (1), (1996), 79-88. | DOI | MR | Zbl
,[162] On small subsets in abelian groups, this volume.
,[163] The structure of multisets with small number of subset sums, this volume.
,[164] A new approach to the general minimum distance decoding problem: the zero neighbors algorithm, IEEE Trans. on Inform. Theory 31(3) (1985), 378-384. | DOI | MR | Zbl
, ,[165] Theorie d'addition des variables aléatoires. | JFM | Zbl
,[166] Groups with automorphisms inverting most elements, Math. Z. 124 (1972), 51-63. | DOI | EuDML | MR | Zbl
, ,[167] On representation of powers by subset-sums, Acta Arithmetica LII (1989), 353-366. | DOI | EuDML | MR | Zbl
,[168] On subset sums of -sets, Discrete Mathematics 114 (1993), 1-3 and 367-377. | DOI | MR | Zbl
,[169] Subset sums of sets of residues, this volume, | Numdam
,[170] The classification of groups with the small squaring property on 3-sets, Bull. Austral. Math. Soc. 46 (1992), 263-269. | DOI | MR | Zbl
, ,[171] On groups in which every product of four elements can be reordered, Arch. Math. 49 (1987), 273-276. | DOI | MR | Zbl
, ,[172] On the derived length of groups with some permutational properties, manuscript.
, ,[173] Classification of groups in which every product of four elements can be reordered, Rend. Sem. Mat. Univ. Padova, 93, (1995), 7-26. | EuDML | Numdam | Zbl
, , ,[174] On the measure of product sets in a topological group, J. London Math. Soc. 35 (1960), 403-407. | DOI | MR | Zbl
,[175] On the measure of sum sets, II, The sum theorem for the torus, Proc. Cambridge Philos. Soc. 49 (1953), 40-43. | DOI | MR | Zbl
,[176] On the measure of sum sets, III, The continuous theorem, Proc. Edinburg Math. Soc. 12(2) (1960/61), 209-211 | MR | Zbl
,On the measure of sum sets, III, The continuous theorem, Proc. Edinburg Math. Soc. correction ibid. 14 (1964/65), 165-166. | DOI | MR | Zbl
,[177] Groups in which a large number of operators may correspond to their inverses, Trans. Amer. Math. Soc. 7 (1906), 233-240. | DOI | JFM | MR
,[178] A proof of the fundamental theorem on the density of sums of sets of positive integers, Ann. Math. 43 (2) (1942), 523-527. | DOI | MR | Zbl
,[179] Additive group theory - a progress report, Bull. Amer. Math. Soc. 79(6) (1973), 1069-1075. | DOI | MR | Zbl
,[180] Two addition theorems, J. Comb. Th. 3 (1967), 233-235. | DOI | MR | Zbl
,[181] Sums of sets in the elementary abelian group of type , J. Comb. Th. 2 (1967), 275-284. | DOI | MR | Zbl
, ,[182] Efficent elementary methods for the dense subset-sum problem, M. Sc. Thesis, Computer Science Department, Tel-Aviv University, 1988.
,[183] A mixture of dynamic programming and branch-and-bound for the subset-sum problem, Management Science 30 (1984), 765-771. | DOI | MR | Zbl
, ,[184] The knapsack problem, in "Combinatorial Optimization", ed : N. Christofides, A. Mingozzi, P. Toth, C. Sandi, Wiley, 1979, 237-279. | MR | Zbl
, ,[185] On product sets in a unimodular group, Proc. Cambridge Philos. Soc. 64 (1968), 1001-1007. | DOI | MR | Zbl
,[186] Giornale dell'Instituto degli Attuari 5 (1934), 483-495.
,[187] Groups which admit five-eight automorphisms, Proc. Nat. Acad. Sci. 17 (1931), 39-43. | DOI | Zbl
,[188] Groups contaning the largest possible number of operators of order two, Amer. Math. Monthly 12 (1905), 149-151. | MR
,[189] Non abelian groups admitting more than half inverse corespondences, Proc. Nat. Acad. Sci. 16 (1930), 168-172. | DOI | JFM
,[190] A note on curvature and the fundamental group, J. Diff. Geom. 2 (1968), 1-7. | DOI | MR | Zbl
,[191] Growth of finitely generated solvable groups, J. Diff. Geom. 2 (1968), 447-449. | DOI | MR | Zbl
,[192] Inequalities for the concentration function, Theory of probability and its applications, 30 (1) (1983), 38-49.
, ,[193] On local limit Theorems I, Litovski Math. Sbor. Vol. 14 num. 4, 129-144, 1974. | MR | Zbl
, ,[194] On local limit Theorems II, Litovski Math. Sbor. 17(4) (1977), 169-179. | MR | Zbl
, ,[195] On product equality preserving mappings in groups, J. Algebra, 182, (1996), no. 3, 653-663. | DOI | MR | Zbl
,[196] A local limit theorem for large deviations in the case of differently distributed lattice summands, Theory of Probability and its Applications 17(4) (1972), 678-684. | DOI | Zbl
,[197] Inverse problems of additive number theory and local limit theorems for lattice random variables, in "Number Theory", Kalinin Gos. Univ. Moscow 1973, 148-162 [Russian]. | MR | Zbl
, , ,[198] On an arithmetic method of obtaining local limit theorems for lattice random variables, Prob. Theor. and its applications 15(1) (1970), 86-96. | DOI | MR | Zbl
, , ,[199] Sumsets of measurable sets, Proc. Amer. Math. Soc. 78 (1) (1980), 59-63. | DOI | MR | Zbl
,[200] Additive Number Theory. Inverse Problems and the Geometry of Sumsets.", Graduate Texts in Mathematics, 165, Springer Verlag, New-York, (1996), xiv+293 pp. | DOI | MR | Zbl
, "[201] Sumsets containing long arithmetic progressions and powers of 2, Acta Arithmetica 46 (1989), 147-154. | DOI | EuDML | MR | Zbl
and ,[202] Inverse theorems and the number of sums and products, this volume, | Numdam | Zbl
, ,[203] Integer and combinatorial optimization", John Wiley k, Sons, 1988. | DOI | MR
, , "[204] On a problem of Paul Erdős in groups, J. Austr. Math. Soc. (Ser. A) 21 (1976), 467-472. | DOI | MR | Zbl
,[205] Stratified Sets, this volume. | Numdam | MR | Zbl
,[206] An addition theorem modulo , J. Comb. Th. 5 (1968), 45-52. | DOI | MR | Zbl
,[207] An Addition Theorem for the Elementary Abelian Group, J. Comb. Th. 5 (1968), 53-58. | DOI | MR | Zbl
,[208] Sums of sets of group elements, Acta Arithmetica, 28 (1975), 147-156. | DOI | EuDML | MR | Zbl
,[209] An addition theorem for finite abelian groups, J. Number Theory 9 (1977), 63-70. | DOI | MR | Zbl
,[210] On a combinatorial problem of Erdős, Ginzberg and Ziv, J. Number theory 8 (1976), 52-57. | DOI | MR | Zbl
,[211] A combinatorial problem on finite abelian groups I and II, J. Number Theory, 1 (1969), 8-11 and 195-199. | DOI | MR | Zbl
,[212] On the sum of two sets in a group, J. Number Theory, 18 (1984), 110-120. | DOI | MR | Zbl
,[213] Alternating parity of Chebyshev Systems, Journal of Approximation Theory 9 (1973), 295-298. | DOI | MR | Zbl
,[214] Introduction to analytic number theory, Izdat. "Nauka", Moscow, 1971. 416 pp. [Russian]. | MR | Zbl
,[215] Additive problems with growing number of summands, IAN, Math. Ser., 20 (1956), 751-764. | MR | Zbl
,[216] On the concentration function, Theory of Probability and its Applications 22(2) (1977), 371-375. | MR | Zbl
, ,[217] An analytic method for estimates of the concentration function, Proceedings of the Steklov Institute of Mathematics 1 (1980). | Zbl
, ,[218] A sharper form of an inequality for the concentration function, Theory Prob. Appl. 23 (1978), 359-362. | DOI | MR | Zbl
, ,[219] The number of pairwise non-commuting elements and the index of the center in a finite group, J. London. Math. Soc. 35(2) (1987), 287-295. | DOI | Zbl
,[220] Das 'Schiefe Produkt' in der Gruppentheorie, Comment. Math. Helvet. 20 (1947), 225-264. | DOI | EuDML | MR | Zbl
,[221] Maximal sum free sets in finite abelian groups, Bull. Austral. Math. Soc. 2 (1970), 289-297. | DOI | MR | Zbl
, ,[222] An estimate for concentration functions, Theory of Probability and its Applications 6 (1961), 94-97. | DOI | Zbl
,[223] Anwendung eines Satzes der additiven Zahlentheorie auf eine Grupenteoretische Frage, Math. Z. 42 (1937), 538-542. | DOI | EuDML | JFM | MR
,[224] On certain sets of integers I, J. London Math. Soc. 28 (1953), 104-109. | DOI | MR | Zbl
,[225] On certain sets of integers II, J. London Math. Soc. 29 (1954), 20-26. | DOI | MR | Zbl
,[226] What is the probability that two elements of a finite group commute?, Pac. J. Math. 2(1) (1979), 237-247. | DOI | MR | Zbl
,[227] The density of the set of sums, Acta Arith.,58, (1991), 169-172. | DOI | EuDML | MR | Zbl
,[228] Sums of finite sets, Number theory (New York seminar, 1991-1995), eds. D. V. Chudnovsky, G. V. Chudnovsky, M. B. Nathanson, Springer, New York, (1996), 281-293. | DOI | MR | Zbl
,[229] On the cardinality of and , in "Combinatorics", Eds. A. Hajnal, V.T. Sos, Coll. Math. Soc. J. Bolyai 18, North Holland 1978, 933-938. | MR | Zbl
,[230] On the number of sums and differences, Acta Math. Hung. 59 (1992), 439-447. | DOI | MR | Zbl
,[231] Sets of sums and differences, in "Proc. de Seminare de Theorie des nombres de Paris (1982-1983)", Birkhauser, Boston 1984, 267-273. | MR | Zbl
,[232] Sums of sets in several dimensions, Combinatorica, 14, (1994), 485-490. | DOI | MR | Zbl
,[233] Generalized arithmetical progressions and sumsets, Acta Math. Hungar., 65, (1994), 379-388. | DOI | MR | Zbl
,[234] Arithmetic progressions in sumsets, Acta Arith. 60(2) (1991), 191-202. | DOI | EuDML | MR | Zbl
,[235] An application of graph theory to additive number theory, Scientia (Series A) Math. Sciences 3 (1989), 97-109. | MR | Zbl
,[236] Sets of sums and commutative graphs, Proc. of the workshop in combinatorics, Bielefeld 1991, Studia Sei. Math. Hungar., 30, (1995), 127-148. | MR | Zbl
,[237] Arithmetic progressions and the number of sums, Period. Math. Hung. 25 (1) (3) (1992), 105-111. | DOI | MR | Zbl
,[238] An analog of Freiman's theorem in groups, this volume. | Zbl
,[239] Finite addition theorems I, J. Number Theory 32 (1) (1989), 114-130 | DOI | MR | Zbl
,[240] Finite addition theorems II, J. Number Theory, 48, (1994), no. 2, 197-218. | DOI | MR | Zbl
,[241] Finite addition theorems III, in "Groupe de Travail en Theorie Analytique et Elementaire des Nombres 1989-1990", Publ. Math. Orsay 1992, 105-122. | MR | Zbl
,[242] Uber additive Eigenschaften von Zahlen, Math. Ann. 107 (1933), 649-690. | DOI | EuDML | JFM | MR | Zbl
,[243] Combinatorial conditions in residually finite groups I, J. Algebra 157 (1) (1993), 43-50. | DOI | MR | Zbl
, ,[244] Combinatorial conditions in residually finite groups II, J. Algebra 157 (1) (1993), 51-62. | DOI | MR | Zbl
,[245] Einheiten quadratischer Formen. | DOI | JFM | Zbl
,[246] Cyclic spaces for Grassman derivatives and additive theory, Bull. London Math. Soc. 26 (1994), 140-146. | DOI | MR | Zbl
and ,[247] On a problem in combinatorical number theory, J. Math. Sci. 1 (1966), 77-80. | MR | Zbl
,[248] On sets of integers containing no elemenents in arithmetic progression, Acta Arithmetica 27 (1975), 199-245. | DOI | EuDML | MR | Zbl
,[249] On a conjecture of Erdos and Heilbronn, Acta Arithmetica 17 (1970), 227-229. | DOI | EuDML | MR | Zbl
,[250] Integer sets containing no arithmetic progression, Math. Acad. Sci. Hungar. 56 (1990), 155-158. | DOI | MR | Zbl
,[251] On complexes in a finite abelian group. Proc. of the Japan Academy 64(7) (Series A) 7 (1988), 245-246. | DOI | MR | Zbl
, ,[252] An inverse additive problem, Math. Sb. 52 (94) (1960), 947-952 [Russian]. | MR | Zbl
,[253] On a generalization of the Minkowsky convex body theorem, J. of Number Theory 13 (1981), 192-209. | DOI | MR | Zbl
,[254] Some estimations useful in the geometry of numbers, Period. Math. Hungar. 11 (1980), 95-103. | DOI | MR | Zbl
,[255] Some remarks about the lattice points in difference sets, in "Proc of A. Haar Memorial Conf. (Budapest, 1985)", Ed. J. Szabados, Coll. Math. Soc. J. Bolyai 49, North-Holland, Amsterdam-New York, 1986, 929-937. | MR | Zbl
,[256] Upper estimates of maximum probability for sums of independent random vectors, Theory of probability and its applications 30(1) (1983), 38-49 [Russian]. | MR | Zbl
,[257] The critical pairs of subsets of a group of prime order, J. London Math. Soc. 31 (1956), 200-205 | DOI | MR | Zbl
,The critical pairs of subsets of a group of prime order see addendum in J. London Math. Soc., 31 (1956), 280-286. | DOI | MR | Zbl
,[258] On groups consisting mostly of involutions, Proc. Cambridge Philos. Soc. 67(2) (1970), 251-262. | DOI | MR | Zbl
,[259] Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Diff. Geom. 2 (1968), 421-446. | DOI | MR | Zbl
,[260] The measure of the large values of the modulus of a trigonometric sum, in "Number theoretic studies in the Markov spectrum and in the structural theory of set addition", Kalinin Gos. Univ., Moscow 1973, 163-171 [Russian]. | MR | Zbl
,[261] On the number of sums and differences, this volume, | Numdam | MR
, , ,[262] Subset sums in binary spaces, Europ. J. Combin., (1992) 13, 221-230. | DOI | MR | Zbl
,[263] A generalisation to non-commutative groups of a theorem of Mann, Discrete Math., 126, (1994), no. 1-3, 365-372. | DOI | MR | Zbl
,[264] An extremal problem related to the covering radius of binary codes, in "First French-Soviet Workshop on algebraic coding", Lecture Notes in Computer Science 573, Springer-Verlag 1992, 42-51. | DOI | MR | Zbl
,[265] Error-correcting -codes, IEEE Trans. on Information Theory 37 (3) (1991), 730-734. | DOI | MR | Zbl
, ,[266] Applications of coding theory to interconnection networks, Discrete Applied Math. 37/38 (1992), 553-562. | DOI | MR | Zbl
, ,[267] Upper estimations for the concentration function in Hilbert space, Theory of Probability and its applications 26 (2) (1982), 328-343. | DOI | MR | Zbl
,[268] Non-averaging sets, in "Combinatorics: conference at Univ. California, Los Angeles, 1968", Proc. Sympos. Pure Math. XIX, Amer. Math. Soc., Providence, R.I. 1971, 215-222. | DOI | MR | Zbl
,