Permutation q-enumeration with the Schur row adder

Abstract

Abstract. We q-enumerate here, by the i-major index, the class of permutations of Sn with largest increasing subsequence of size n − k and increasing rst n − k entries. The result is obtained by a surprisingly straightforward use of the Schur row adder. Some closely related open problems are also included. Mathematics Subject Classi cation(2000). 05A15