no. 5
On the Horton-Strahler number for random tries
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 5, pp. 443-456 
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     author = {Devroye, L. and Kruszewski, P.},
     title = {On the {Horton-Strahler} number for random tries},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {443--456},
     year = {1996},
     publisher = {EDP Sciences},
     volume = {30},
     number = {5},
     mrnumber = {1435732},
     zbl = {0867.68087},
     language = {en},
     url = {https://www.numdam.org/item/ITA_1996__30_5_443_0/}
}
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Devroye, L.; Kruszewski, P. On the Horton-Strahler number for random tries. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 30 (1996) no. 5, pp. 443-456. https://www.numdam.org/item/ITA_1996__30_5_443_0/

1 A. V. Aho. , J. E. Hopcroft and J. D. Ullman, Data Structures and Algorithms, Addison-Wesley, Reading, MA, 1983. | Zbl | MR

2 D. Arquès, N. Janey and X. G. Viennot Modélisation de la croissance et de la forme de structures arborescentes par matrice d'évolution. In Actes de MICAD'91, Paris, 1991, pp. 321-336.

3. L. Devroye, A note ontheprobabilistic analysis of Patricia trees, Random Structures and Algorithms, 1992, 3, pp. 203-214 | Zbl | MR

4. L. Devroye and P. Kruszewski, A note on the Horton-Strahler number for random trees, Information Processing Letters, 1994, 52, pp. 155-159. | Zbl | MR

5. A. P. Ershov, On programming of arithmetic operations, Communications of the ACM, 1958, 1, pp. 3-6. | Zbl

6. R. Fagin, J. Nievergelt, N. Pippenger and H. R. Strong, Extendible hashing - a fast access method for dynamic files, ACM Transactions on Database Systems, 1979, 4, pp. 315-344.

7. P. Flajolet, J. C. Raoult and J. Vuillemin, The number of registers required for evaluating arithmetic expressions, Theoretical Computer Science, 1979, 9, pp. 99-125. | Zbl | MR

8. J. Françon, Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique, RAIRO Theoretical Informatics, 1984, 18, pp. 355-364. | Zbl | MR | Numdam

9. E. H. Fredkin, Trie memory, Communications of the ACM, 1960, 3, pp. 490-500.

10. W. Hoeffding, Probability inequalities for sums of bounded random variables, Journal of the American Statistical Association, 1963, 58, pp. 13-30. | Zbl | MR

11. R. E. Horton, Erosional development of streams and their drainage basins; hydrophysical approach to quantitative morphology, Bulletin of the Geological Society of America, 1945, 56, pp. 275-370.

12. P. Jacquet and W. Szpankowski, Analysis of digital tries with Markovian dependency, IEEE Transactions on Information Theory, 1991, IT37, pp. 1470-1475.

13. R. Kemp, The average number of registers needed to evaluate a binary tree optimally, Acta Informatica, 1979, 11, pp. 363-372. | Zbl | MR

14. D. E. Knuth, The Art of Computer Programming. Sorting and Searching, volume 3, Addison-Wesley, Reading, MA, 1973. | MR

15. P. Kruszewski, A probabilistic exploration of the Horton-Strahler number for random binary trees, Master's thesis, School of Computer Science, McGill University, 1993.

16. P. A. Larson, Dynamic hashing. BIT, 1978, 75, pp. 184-201. | Zbl | MR

17. W. Litwin, Trie hashing. In Proceedings of the ACM - SIGMOD Conf. MOD., Ann Arbor, Michigan, 1981.

18. A. Meir and J. W. Moon, Stream lengths in random channel networks, Congressus Numerantium, 1980, 33, pp. 25-33. | Zbl | MR

19. A. Meir, J. W. Moon and J. R. Pounder, On the order of random channel networks, SIAM Journal of Algebraic and Discrete Methods, 1980, 1, pp. 25-33. | Zbl | MR

20. J. W. Moon, On Horton's law for random channel networks, Annals of Discrete Mathematics, 1980, 8, pp. 117-121. | Zbl | MR

21. J. G. Penaud, Matrice de ramification des arbres binaires, Discrete Applied Mathematics, 1991, 31, pp. 1-21. | Zbl | MR

22. B. Pittel, Asymptotic growth of a class of random trees, Annals of Probability, 1985, 18, pp. 414-427. | Zbl | MR

23. H. Prodinger, Solution of a problem of Yekutieli and Mandelbrot, Technical report, Technical University of Vienna, Austria, 1995.

24. A. N. Strahler, Hypsometric (area-altitude) analysis of erosional topology, Bulletin of the Geological Society of America, 1952, 63, pp. 1117-1142.

25. J. Vannimenus and X. G. Viennot, Combinatorial Tools for the Analysis of Ramified Patterns, Journal of Statistical Physics, 1989, 54, pp. 1529-1539. | MR

26. M. Vauchaussade De Chaumont, Nombre de Strahler des arbres, langages algébriques et dénombrement des structures secondaires en biologie moléculaire, PhD thesis, Université de Bordeaux I, 1985.

27. M. Vauchaussade De Chaumont and X. G. Viennot, Enumeration of RNAs secondary structures by complexity, Mathematics in Medicine and Biology, Lecture Notes in Biomathematics, 1985, 57, pp. 360-365. | Zbl

28. X. G. Viennot, Trees everywhere. In A. Arnold ed., Proceedings of the 15th Colloquium on Trees in Algebra and Programming, Copenhagen, Denmark, May 15-18, 1990, Lecture Notes in Computer Science, Springer-Verlag, Berlin 1990, volume 431, pp. 18-41. | Zbl | MR

29. X. G. Viennot, G. Eyrolles, N. Janey and D. Arquès, Combinatorial analysis of ramified pattems and computer imagery of trees. In Proceedings of SIGGRAPH'89, Computer Graphics, 1989, volume 23, pp. 31-40.