On the Horton-Strahler number for combinatorial tries

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1. [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions. Dover (1970). 
2. [2] T. M. Apostol, Introduction to Analytic Number Theory. Springer (1976). Zbl0335.10001MR434929
3. [3] N. G. de Bruijn, D. E. Knuth and S. O. Rice, The Average Height of Planted Plane Trees. Graph Theory and Computing, edited by R.C. Read. Academic Press (1972). Zbl0247.05106MR505710
4. [4] L. Devroye and P. Kruszewski, On the Horton-Strahler Number for Random Tries. Theoret. Informatics Appl. 30 (1996) 443-456. Zbl0867.68087MR1435732
5. [5] M. Drmota, Asymptotic Distributions and a Multivariate Darboux Method in Enumeration Problems. J. Combin. Theory Ser. A 67 (1994) 169-184. Zbl0801.60016MR1284406
6. [6] A. P. Ershov, On Programming of Arithmetic Operations. Comm. ACM 1 (1958 3-6. Zbl0086.33203
7. [7] P. Flajolet, J. C. Raoult and J. Vuillemin, The Number of Registers required for Evaluating Arithmetic Expressions. Theoret. Comput. Sci. 9 (1979) 99-125. Zbl0407.68057MR535127
8. [8] P. Flajolet and A. Odlyzko, Singularity Analysis of Generating Functions. SIAM J. Discrete Math. 3 (1990) 216-240. Zbl0712.05004MR1039294
9. [9] P. Flajolet and H. Prodinger, Register Allocation for Unary-Binary Trees. SIAM J. Comput. 15 (1986) 629-640. Zbl0612.68065MR850413
10. [10] P. Flajolet, X. Gourdon and P. Dumas, Mellin transforms and asymptotics: Harmonic sums. Theoret Comput. Sci. 144 (1995) 3-58. Zbl0869.68057MR1337752
11. [11] J. Françon, Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique. Theoret. Informatics Appl. 18 (1984) 355-364. Zbl0547.68041MR775838
12. [12] R. E. Horton, Erosioned development of systems and their drainage basins, hydrophysical approach to quantitative morphology. Bull. Geol. Soc. of America 56 (1945) 275-370. 
13. [13] R. Kemp, The Average Number of Registers Needed to Evaluate a Binary Tree Optimally. Acta Inform. 11 (1979) 363-372. Zbl0395.68059MR533482
14. [14] R. Kemp, A Note on the Stack Size of Regularly Distributed Binary Trees. BIT 20 (1980) 157-163. Zbl0428.68076MR583031
15. [15] R. Kemp, Fundamentals of the Average Case Analysis of Particular Algorithms. Wiley-Teubner Series in Computer Science (1984). Zbl0638.68026MR786659
16. [16] R. Kemp, On the Stack Ramification of Binary Trees. Random Graphs 2 (1992) 117-138. Zbl0825.68492MR1166611
17. [17] D. E. Knuth, The Art of Computer Programming, Volume 1: Fundamental Algorithms, 3rd Ed. Addison-Wesley (1997). Zbl0895.68055MR378456
18. [18] A. Meir, J. W. Moon and J. R. Pounder, On the Order of Random Channel Networks. SIAM J. Algebraic Discrete Math. 1 (1980) 25-33. Zbl0496.94020MR563011
19. [19] M. E. Nebel, New Results on the Stack Ramification of Binary Trees. J. Autom. Lang. Comb. 2 (1997) 161-175. Zbl0895.68071MR1611168
20. [20] M. E. Nebel, The Stack-Size of Tries, A Combinatorial Study. Theoret. Comput. Sci. (to appear). Zbl0988.68137MR1871080
21. [21] M. E. Nebel, The Stack-Size of Uniform Random Tries Revisited (submitted). Zbl0995.68071
22. [22] A. N. Strahler, Hypsometric (area-altitude) analysis of erosonal topology. Bull. Geol. Soc. of America 63 (1952) 1117-1142.