Determinantal formulas with major indices
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.
Proceedings of the American Mathematical Society
Digital Object Identifier (DOI)
McConville, Thomas; Robertson, Donald; and Smyth, Clifford, "Determinantal formulas with major indices" (2021). Faculty Publications. 5317.