A recursion formula for k-Schur functions

TL;DR

This paper introduces a recursion formula for k-Schur functions at t=1 using combinatorial operators that generalize Bernstein operators, providing a new way to interpret their expansion coefficients.

Contribution

It presents a novel recursion formula for k-Schur functions at t=1 based on generalized combinatorial operators, extending the classical Bernstein operator approach.

Findings

Recursion formula for k-Schur functions at t=1

Combinatorial interpretation of expansion coefficients

Generalization of Bernstein operators

Abstract

The Bernstein operators allow to build recursively the Schur functions. We present a recursion formula for k-Schur functions at t=1 based on combinatorial operators that generalize the Bernstein operators. The recursion leads immediately to a combinatorial interpretation for the expansion coefficients of k-Schur functions at t=1 in terms of homogeneous symmetric functions.