On finite addition theorems
Structure theory of set addition, Astérisque, no. 258 (1999), pp. 109-127 
@incollection{AST_1999__258__109_0,
     author = {S\'ark\H{o}zy, Andr\'as},
     title = {On finite addition theorems},
     booktitle = {Structure theory of set addition},
     editor = {Deshouilliers Jean-Marc and Landreau Bernard and Yudin Alexander A.},
     series = {Ast\'erisque},
     pages = {109--127},
     year = {1999},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {258},
     mrnumber = {1701190},
     zbl = {0969.11003},
     language = {en},
     url = {https://www.numdam.org/item/AST_1999__258__109_0/}
}
TY  - CHAP
AU  - Sárkőzy, András
TI  - On finite addition theorems
BT  - Structure theory of set addition
AU  - Collectif
ED  - Deshouilliers Jean-Marc
ED  - Landreau Bernard
ED  - Yudin Alexander A.
T3  - Astérisque
PY  - 1999
SP  - 109
EP  - 127
IS  - 258
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_1999__258__109_0/
LA  - en
ID  - AST_1999__258__109_0
ER  - 
%0 Book Section
%A Sárkőzy, András
%T On finite addition theorems
%B Structure theory of set addition
%A Collectif
%E Deshouilliers Jean-Marc
%E Landreau Bernard
%E Yudin Alexander A.
%S Astérisque
%D 1999
%P 109-127
%N 258
%I Société mathématique de France
%U https://www.numdam.org/item/AST_1999__258__109_0/
%G en
%F AST_1999__258__109_0
Sárkőzy, András. On finite addition theorems, dans Structure theory of set addition, Astérisque, no. 258 (1999), pp. 109-127. https://www.numdam.org/item/AST_1999__258__109_0/

[1] N. Alon, Subset sums, J. Number Theory, 27, 1987, 196-205. | MR | Zbl | DOI

[2] N. Alon and G. Freiman, On sums of subsets of a set of integers, Combinatorica, 8, 1988, 297-306. | MR | Zbl | DOI

[3] F. Dyson, A theorem on the densities of sets of integers, J. London Math. Soc., 20, 1945, 8-14. | MR | Zbl | DOI

[4] P. Erdős, On the representation of large integers as sums of distinct summands taken from a fixed set, Acta. Arith., 7, 1961/62, 345-354. | MR | Zbl | EuDML | DOI

[5] P. Erdős and G. Freiman, On two additive problems, J. Number Theory, 34, 1990, 1-12. | MR | Zbl | DOI

[6] P. Erdős, J.-L. Nicolas and A. Sárkőzy, On the number of partitions of n without a given subsum, II, Analytic Number Theory, Proceedings of a Conference in Honor of P. T. Bateman, B. C. Berndt et al. eds., Birkhäuser, Boston-Basel-Berlin, 1990, 205-234. | MR | Zbl

[7] P. Erdős, J.-L. Nicolas and A. Sárkőzy, On the number of pairs of partitions of n without common subsums, Colloquium Math., 63, 1992, 61-83. | MR | Zbl | EuDML

[8] P. Erdős and A. Sárkőzy, On a problem of Straus, Disorder in Physical Systems (a volume in Honour of John M. Hammersley), G. R. Grimmett and D. J. Welsh eds., Clarendon Press, Oxford, 1990, 55-66. | Zbl

[9] P. Erdős and A. Sárkőzy, Arithmetic progression in subset sums, Discrete Mathematics, 102, 1992, 249-264. | MR | Zbl | DOI

[10] P. Erdős, A. Sárkőzy and C. L. Stewart, On prime factors of subset sums, J. London Math. Soc., 49, 1994, 209-218. | MR | Zbl | DOI

[11] J. Folkman, On the representation of integers as sums of distinct terms from a fixed sequence, Canadian J. Math, 18, 1966, 643-655. | MR | Zbl | DOI

[12] G. A. Freiman, Foundations of a Structural Theory of Set Additions, Translations of Mathematical Monographs, 37, Amer. Math. Soc., Providence, RI. | MR | Zbl

[13] G. A. Freiman, New analytical results in subset-sum problem, Discrete Mathematics, 114, 1993, 205-218. | MR | Zbl | DOI

[14] G. A. Freiman, Sumsets and powers of 2 , Coll. Math. Soc. J. Bolyai, 60, 1992, 279-286. | MR | Zbl

[15] H. Halberstam and H.-E. Richert, Sieve Methods, Academic Press, 1974. | MR | Zbl

[16] H. Halberstam and K. F. Roth, Sequences, Springer Verlag, Berlin, 1983. | MR | Zbl | DOI

[17] A. Khintchin, Zur additiven Zahlentheorie, Math. Sb. N.S., 39, 1932, 27-34. | Zbl | JFM

[18] M. Kneser, Abschätzungen der asymptotischen Dichte von Summenmengen, Math. Z, 58, 1953, 459-484. | MR | Zbl | EuDML | DOI

[19] H. B. Mann, A proof of the fundamental theorem on the density of sums of sets of positive integers, Ann. Math., 43, 1942, 523-527. | MR | Zbl | DOI

[20] M. B. Nathanson and A. Sárkőzy, Sumsets containing long arithmetic progressions and powers of 2 , Acta Arith., 54, 1989, 147-154. | MR | Zbl | EuDML | DOI

[21] A. Sárkőzy, Finite addition theorems, I, J. Number Theory, 32, 1989, 114-130. | MR | Zbl | DOI

[22] A. Sárkőzy, Finite addition theorems, II, J. Number Theory, 48, 1994, 197-218. | MR | Zbl | DOI

[23] A. Sárkőzy, Finite addition theorems, III, Publ. Math. d'Orsay, 92-01, 105-122 | MR | Zbl

[24] L. G. Schnirelmann Über additive Eigenschaften von Zahlen, Annals Inst. Polyt. Novocherkassk, 14, (1930), 3-28 | JFM

L. G. Schnirelmann Über additive Eigenschaften von Zahlen, Math. Annalen, 107, 1933, 649-90. | MR | Zbl | EuDML | JFM | DOI