MacMahon-type Identities for Signed Even Permutations

2004/05/18 by Dan Bernstein
Mathematics · #math.CO #msc:05A15 #msc:05A19

paper · pdf

published as Electronic Journal of Combinatorics 11 (2004), #R83 · 16 pages

arxiv created 2004/05/18 · arxiv updated 2009/12/01

Abstract

MacMahon's classic theorem states that the 'length' and 'major index' statistics are equidistributed on the symmetric group S_n. By defining natural analogues or generalizations of those statistics, similar equidistribution results have been obtained for the alternating group A_n by Regev and Roichman, for the hyperoctahedral group B_n by Adin, Brenti and Roichman, and for the group of even-signed permutations D_n by Biagioli. We prove analogues of MacMahon's equidistribution theorem for the group of signed even permutations and for its subgroup of even-signed even permutations.

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