MacMahon-type Identities for Signed Even Permutations
Abstract
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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.