On Counting Permutations by Pairs of Congruence Classes of Major Index
On Counting Permutations by Pairs of Congruence Classes of Major Index
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 $\sigma.$ Fix positive integers $k < \ell\leq n,$ and nonnegative integers $i,j.$ Let $m_n(i\backslash k; j\backslash \ell)$ denote the cardinality of the …