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MacMahon-type Identities for Signed Even Permutations

Dan Bernstein
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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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Dan Bernstein. 2004-05-18. MacMahon-type Identities for Signed Even Permutations. https://arxiv.org/abs/math/0405346

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