Descents of permutations in a ferrers board - Texas A&M University (TAMU) Scholar

The classical Eulerian polynomials are defined by setting, where A n,k is the number of permutations of length n with k - 1 descents. Let be the inv q-analogue of the classical Eulerian polynomials whose generating function is well known, In this paper we consider permutations restricted in a Ferrers board and study their descent polynomials. For a general Ferrers board F, we derive a formula in the form of permanent for the restricted q-Eulerian polynomial, If the errers board has the special shape of an nn square with a triangular board of size s removed, we rove that A F (t; q) is a sum of s + 1 terms, each satisfying an equation that is similar to (0.1). Then we apply our results to permutations with bounded drop (or excedance) size, for which the descent polynomial was first studied by Chung et al.

Descents of permutations in a ferrers board Academic Article