On counting permutations by pairs of congruence classes of major index
Combinatorics
2007-05-23 v1
Abstract
For a fixed positive integer n, let S_n denote the symmetric group of n! permutations on n symbols, and let maj(sigma) denote the major index of a permutation sigma. For positive integers k<m not greater than n and non-negative integers i and j, we give enumerative formulas for the cardinality of the set of permutations sigma in S_n with maj(sigma) congruent to i mod k and maj(sigma^(-1)) congruent to j mod m. When m divides n-1 and k divides n, we show that for all i,j, this cardinality equals (n!)/(km).
Cite
@article{arxiv.math/0109205,
title = {On counting permutations by pairs of congruence classes of major index},
author = {Helene Barcelo and Robert Maule and Sheila Sundaram},
journal= {arXiv preprint arXiv:math/0109205},
year = {2007}
}
Comments
8 pages