A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets

Sen Peng Eu, Tung Shan Fu, Hsiang Chun Hsu

Research output: Contribution to journalArticle

Abstract

We present a simple transformation for the inversion number and major index statistics on the labelings of a rooted tree with n vertices in the form of a rake with k teeth. The special case k= 0 provides a simple transformation for the Mahonian statistics on the set Sn of permutations of { 1 , 2 , ⋯ , n}. We also extend the transformation to a bijective interpretation of the fact that the major index of the equivalence classes of the labelings is equidistributed with the major index of the permutations in Sn satisfying the condition that the elements 1 , 2 , ⋯ , k appear in increasing order.

LanguageEnglish
Pages373-381
Number of pages9
JournalGraphs and Combinatorics
Volume34
Issue number2
DOIs
Publication statusPublished - 2018 Mar 1

Fingerprint

Major Index
Poset
Labeling
Statistics
Equivalence classes
Permutation
Rooted Trees
Bijective
Equivalence class
Inversion

Keywords

  • Bijection
  • Mahonian statistics
  • Rake poset
  • Subexcedent word

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this

A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets. / Eu, Sen Peng; Fu, Tung Shan; Hsu, Hsiang Chun.

In: Graphs and Combinatorics, Vol. 34, No. 2, 01.03.2018, p. 373-381.

Research output: Contribution to journalArticle

Eu, Sen Peng ; Fu, Tung Shan ; Hsu, Hsiang Chun. / A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets. In: Graphs and Combinatorics. 2018 ; Vol. 34, No. 2. pp. 373-381.
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