A simple transformation for Mahonian statistics on labelings of rake posets

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Title:	A simple transformation for Mahonian statistics on labelings of rake posets
Authors:	Sen-Peng Eu, Tung-Shan Fu, Hsiang-Chun Hsu
Keywords:	Mahonian statistics;Rake poset;Subexcedent word;Bijection
Date:	2018-03
Issue Date:	2019-03-09 12:10:33 (UTC+8)
Publisher:	Springer Japan
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.
Relation:	Graphs and Combinatorics 34(2), p.373-381
DOI:	10.1007/s00373-018-1882-z
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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