On binary trees and Dyck paths

A. Panayotopoulos; A. Sapounakis

Mathématiques et Sciences Humaines (1995)

  • Volume: 131, page 39-51
  • ISSN: 0987-6936

Abstract

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A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.

How to cite

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Panayotopoulos, A., and Sapounakis, A.. "On binary trees and Dyck paths." Mathématiques et Sciences Humaines 131 (1995): 39-51. <http://eudml.org/doc/94471>.

@article{Panayotopoulos1995,
abstract = {A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.},
author = {Panayotopoulos, A., Sapounakis, A.},
journal = {Mathématiques et Sciences Humaines},
keywords = {binary trees; Dyck paths},
language = {eng},
pages = {39-51},
publisher = {Ecole des hautes-études en sciences sociales},
title = {On binary trees and Dyck paths},
url = {http://eudml.org/doc/94471},
volume = {131},
year = {1995},
}

TY - JOUR
AU - Panayotopoulos, A.
AU - Sapounakis, A.
TI - On binary trees and Dyck paths
JO - Mathématiques et Sciences Humaines
PY - 1995
PB - Ecole des hautes-études en sciences sociales
VL - 131
SP - 39
EP - 51
AB - A bijection between the set of binary trees with n vertices and the set of Dyck paths of length 2n is obtained. Two constructions are given which enable to pass from a Dyck path to a binary tree and from a binary tree to a Dyck path.
LA - eng
KW - binary trees; Dyck paths
UR - http://eudml.org/doc/94471
ER -

References

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  1. [1] Hilton, P., Pedersen, J., "Catalan numbers, their generalization and their uses", The Mathematical Intelligencer, 2 (1991), 64-75. Zbl0767.05010MR1098222
  2. [2] Lalanne, J.C., "q-Bessel, arbres, et chemins valués ", J. Combin. Theory, Ser. A60 (1992), 225-245. Zbl0754.05033MR1168155
  3. [3] Panayotopoulos, A., Sapounakis, A., "On binary trees and permutations", Math. Inf. Sci. hum., 117 (1992), 61-70. Zbl0846.05021MR1164609
  4. [4] Rosenstiehl, P., "Scaffold permutations", Discrete Math., 75 (1989), 335-342. Zbl0668.05001MR1001406

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