A Pieri rule for skew shapes

TL;DR

This paper extends the classical Pieri rule to skew shapes, providing a combinatorial rule for multiplying skew Schur functions by single row Schur functions, with a purely combinatorial proof.

Contribution

It introduces a new Pieri rule for skew shapes and offers a combinatorial proof, expanding the understanding of Schur function multiplication.

Findings

Provides a combinatorial Pieri rule for skew Schur functions

Extends classical Pieri rule to skew shapes

Offers a purely combinatorial proof

Abstract

The Pieri rule expresses the product of a Schur function and a single row Schur function in terms of Schur functions. We extend the classical Pieri rule by expressing the product of a skew Schur function and a single row Schur function in terms of skew Schur functions. Like the classical rule, our rule involves simple additions of boxes to the original skew shape. Our proof is purely combinatorial and extends the combinatorial proof of the classical case.