Quasisymmetric (k,l)-hook Schur functions

TL;DR

This paper introduces a quasisymmetric generalization of hook Schur functions, explores their combinatorial properties, and demonstrates their algebraic behavior, extending classical symmetric function theory.

Contribution

It defines quasisymmetric (k,l)-hook Schur functions and establishes their decomposition, combinatorial relationships, and multiplication properties with classical hook Schur functions.

Findings

Decomposition of hook Schur functions into quasisymmetric versions

Relationship to Gessel's fundamental quasisymmetric functions

Multiplication rules analogous to classical 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. We examine the combinatorics of the quasisymmetric hook Schur functions, providing a relationship to Gessel's fundamental quasisymmetric functions and an analogue of the Robinson-Schensted-Knuth algorithm. We also prove that the multiplication of quasisymmetric hook Schur functions with hook Schur functions behaves the same as the multiplication of quasisymmetric Schur functions with Schur functions.