Pleine trees and reduction rules

Nelson Y. Li; Toufik Mansour; Augustine O. Munagi

Pleine trees and reduction rules

Nelson Y. Li, Toufik Mansour, Augustine O. Munagi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Inspired by the results of Gelfand, Graev and Postnikov (1997) on the reduction rule for binary trees, we present several bijections on different types of reduction rules for plane trees such as symmetric k-ary trees, locally symmetric k-ary trees, symmetric even trees, symmetric noncrossing trees and Motzkin trees. We give the corresponding enumeration results, and prove the equidistribution of some classes of trees.

Original language	English
Pages (from-to)	215-230
Number of pages	16
Journal	Utilitas Mathematica
Volume	81
State	Published - Mar 2010

Keywords

Catalan numbers
Even trees
Motzkin numbers
Noncrossing trees
Reduction rules
Ternary trees
k-ary trees

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Cite this

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AU - Mansour, Toufik

AU - Munagi, Augustine O.

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AB - Inspired by the results of Gelfand, Graev and Postnikov (1997) on the reduction rule for binary trees, we present several bijections on different types of reduction rules for plane trees such as symmetric k-ary trees, locally symmetric k-ary trees, symmetric even trees, symmetric noncrossing trees and Motzkin trees. We give the corresponding enumeration results, and prove the equidistribution of some classes of trees.

KW - Catalan numbers

KW - Even trees

KW - Motzkin numbers

KW - Noncrossing trees

KW - Reduction rules

KW - Ternary trees

KW - k-ary trees

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M3 - Article

AN - SCOPUS:79251605856

SN - 0315-3681

VL - 81

SP - 215

EP - 230

JO - Utilitas Mathematica

JF - Utilitas Mathematica

ER -

Pleine trees and reduction rules

Abstract

Keywords

ASJC Scopus subject areas

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