MacMahon-type Identities for Signed Even Permutations

MacMahon’s classic theorem states that the length and major index statistics are equidistributed on the symmetric group Sn. By defining natural analogues or generalizations of those statistics, similar equidistribution results have been obtained for the alternating group An by Regev and Roichman, for the hyperoctahedral group Bn by Adin, Brenti and Roichman, and for the group of even-signed permutations Dn 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.