Determinantal formulas with major indices

McConville, Thomas; Robertson, Donald; Smyth, Clifford

doi:10.1090/proc/15624

Determinantal formulas with major indices
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by Thomas McConville, Donald Robertson and Clifford Smyth

Proc. Amer. Math. Soc. 149 (2021), 5101-5117

DOI: https://doi.org/10.1090/proc/15624

Published electronically: September 24, 2021

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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.

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