A generalization of descent polynomials

Abstract

The notion of a descent polynomial, a function in enumerative combinatorics that counts permutations with specific properties, enjoys a revived recent research interest due to its connection with other important notions in combinatorics, viz. peak polynomials and symmetric functions. We define the function d m(I, n) as a generalization of the descent polynomial and obtain an explicit formula for d m(I, n) when m is sufficiently large.