A strahler bijection between dyck paths and planar trees

Discrete Mathematics

Volumn 246, Issue 1-3, 2002, Pages 317-329

  Viennot, Xavier Gérard ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32344449037     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0012-365x(01)00265-5     Document Type: Article

References (25)

1. F. Bergeron, G. Labelle, P. Leroux, in: G.C. Rota (Ed.), Combinatorial Species and Tree-Like Structures, Encyclopedia of Mathematics and its Applications, Vol. 67, Cambridge University Press, Cambridge, 1998.
2. J. Berstel, Contribution àl'étude des propriétés arithmétiques des langages formels, Thèse Doctorat d'État, Université Paris VI, 1972.
3. T.S. Chihara, An Introduction to Orthogonal Polynomial, Gordon and Breach, New York, 1978.
4. M. Delest, Polyominoes and animals: some recent results, J. Math. Chem. 8 (1991) 3-18.
5. P.-G. de Gennes, in: C. Domb, M.S. Green (Eds.), Phase Transition and Critical Phenomena, Vol. 3, Academic Press, London, 1976.
6. P. Flajolet, Combinatorial aspects of continued fractions, Discrete Math. 32 (1980) 125-161.
7. P. Flajolet, J.C. Raoult, J. Vuillemin, The number of registers required for evaluating arithmetic expressions, Theoret. Comput. Sci. 9 (1979) 99-125.
8. P. Flajolet, J.S. Vitter, Average case analysis of algorithms and data structures, in: J. van Leemven (Ed.),Handbook of Theoretical Computer Science, Elsevier, Amsterdam, 1990, pp. 431-524.
9. J. Françon, Sur le nombre de registres nécessaires l'évaluation d'une expression arithmétique, RAIRO Inform. Theor. 18 (1984) 355-364.
10. R.E. Horton, Erosioned development of systems and their drainage basins, hydrophysical approach to quantitative morphomology, Bull. Geol. Soc. Amer. 56 (1945) 275-370.
11. R. Kemp, The average number of registers needed to evaluate a binary tree optimally, Acta Inform. 11 (1979) 363-372.
12. G. Kreweras, Sur les éventails de segments, Cahiers du BÜRO. 15 (1970) 3-41.
13. G. Labelle, Combinatoire Énumérative, in: G. Labelle, P. Leroux (Eds.), Proceedings, Montréal, Québec, 1985, Lecture Notes in Mathematics, Vol. 1234, Springer, Berlin, 1986.
14. Mitiko Go, Statistical mechanics of biopolymers and its applications to the melting transition of polynucleotides, J. Phys. Soc. Japan 23 (3) (1967).
15. C. Reutenauer, Dimension and characters of the derived series of the free Lie algebra, in: M. Lothaire (Ed.), Mots, Mélanges offerts àM.-P. Schützenberger, Hermès, Paris, 1990, pp. 171-184.
16. A.N. Strahler, Hypsometrie (area-altitude) analysis of erosional topology, Bull. Geol. Soc. Amer. 63 (1952) 117-1142.
17. P. Striegler, P. Carbon, J.P. Ebel, C. Ehresmann, A general secondary structure model for procaryotic and eucaryotic RNAs of the small ribosomal subunits, European J. Biochem. 120 (1981) 487-495.
18. J. Vannimenus, X.G. Viennot, Combinatorial analysis of physical ramified patterns, J. Statist. Phys. 54 (1989) 1529-1538.
19. M. Vauchaussade de Chaumont, X.G. Viennot, Enumeration of RNAs secondary structures by complexity, in: V. Capasso, E. Grosso, S.L. Paven-Fontana (Eds.), Mathematics in Medicine and Biology, Lecture Notes in Biomathematics, Vol. 57, Springer, Berlin, 1985, pp. 360-365.
20. M. Vauchaussade de Chaumont, X.G. Viennot, Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Proceedings of the Séminaire Lotharingien de Combinatoire, Sainte-Croix-aux-Mines, Université de Strasbourg, 1983.
21. X.G. Viennot, Une Théorie Combinatoire des Polynômes Orthogonaux, Notes de conférences, UQAM, Montréal, 1983, 217 p.
22. X.G. Viennot, Trees everywhere, in: A. Arnold (Ed.), Proceedings of the 15th CAAP, Copenhagen, May 1990, Lecture Notes in Computer Science, Vol. 431, Springer, Berlin, 1990, pp. 18-41.
23. X.G. Viennot, G. Eyrolles, N. Janey, D. Arqués, Combinatorial analysis of ramified patterns and computer imagery of trees, Proceedings of the SIGGRAPH'89; Comput. Graphics 23 (1989) 31-40.
24. M.S. Waterman, Secondary structure of single stranded nucleic acids, in: G.-C. Rota (Ed.), Studies on Foundations and Combinatorics, Adv. in Maths Suppl. Studies, Vol. 1 (1978), pp. 167-212.
25. D. Zeilberger, A bijection from ordered trees to binary trees that sends the pruning order to the Strahler number, Discrete Math. 82 (1990) 89-92.