On counting permutations by pairs of congruence classes of major index

2001/09/26 by Helene Barcelo, Barcelo, Helene, Robert Maule +3
Mathematics · #05A99 #05E99 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A99 #msc:05E99

paper · pdf · doi:10.48550/arxiv.math/0109205

8 pages

arxiv created 2001/09/26 · arxiv updated 2009/11/30

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).

Related

• Counting permutations by congruence class of major index
• Counting occurences of 132 in a permutation
• Major index distribution over permutation classes
• Number of permutations with same peak set for signed permutations
• Coprime Permutations