Determinantal formulas with major indices

Department

Mathematics

Document Type

Article

Publication Date

1-1-2021

Abstract

We give an elementary proof of a major index determinant formula discovered by Krattenthaler and first proved by Thibon using noncommutative symmetric functions. We do so by proving a factorization of an element in the group ring of the symmetric group. By applying similar methods to the groups of signed permutations and colored permutations, we prove determinantal formulas in these groups as conjectured by Krattenthaler.

Journal Title

Proceedings of the American Mathematical Society

Journal ISSN

00029939

Volume

149

Issue

12

First Page

5101

Last Page

5117

Digital Object Identifier (DOI)

10.1090/proc/15624

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