Quasisymmetric (k,l)-hook Schur functions

Abstract

We introduce a quasisymmetric generalization of Berele and Regev's hook Schur functions and prove that these new quasisymmetric hook Schur functions decompose the hook Schur functions in a natural way. In this paper we examine the combinatorics of the quasisymmetric hook Schur functions, providing analogues of the Robinson-Schensted-Knuth algorithm and a generalized Cauchy Identity.

Keywords

• quasisymmetric functions
• schur functions
• tableaux
• rsk
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]