# A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets

A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets 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\$\$ k = 0 provides a simple transformation for the Mahonian statistics on the set \$\$\mathfrak {S}_n\$\$ S n of permutations of \$\$\{1,2,\dots ,n\}\$\$ { 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 \$\$\mathfrak {S}_n\$\$ S n satisfying the condition that the elements \$\$1,2,\dots ,k\$\$ 1 , 2 , ⋯ , k appear in increasing order. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Graphs and Combinatorics Springer Journals

# A Simple Transformation for Mahonian Statistics on Labelings of Rake Posets

, Volume 34 (2) – Feb 26, 2018
9 pages

Publisher
Springer Journals
Copyright © 2018 by Springer Japan KK, part of Springer Nature
Subject
Mathematics; Combinatorics; Engineering Design
ISSN
0911-0119
eISSN
1435-5914
D.O.I.
10.1007/s00373-018-1882-z
Publisher site
See Article on Publisher Site

### 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\$\$ k = 0 provides a simple transformation for the Mahonian statistics on the set \$\$\mathfrak {S}_n\$\$ S n of permutations of \$\$\{1,2,\dots ,n\}\$\$ { 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 \$\$\mathfrak {S}_n\$\$ S n satisfying the condition that the elements \$\$1,2,\dots ,k\$\$ 1 , 2 , ⋯ , k appear in increasing order.

### Journal

Graphs and CombinatoricsSpringer Journals

Published: Feb 26, 2018

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