Classifying the near-equality of ribbon Schur functions

TL;DR

This paper classifies specific pairs of ribbon Schur functions whose difference is a single Schur function, providing identities and conditions for Schur-positivity based on their combinatorial structure.

Contribution

It fully classifies five infinite families of ribbon Schur function pairs with differences equal to a single Schur function and establishes conditions for Schur-positivity.

Findings

Identified five infinite families with difference equal to a single Schur function

Proved an identity relating differences of ribbon Schur functions

Derived necessary conditions for Schur-positivity based on structure

Abstract

We consider the problem of determining when the difference of two ribbon Schur functions is a single Schur function. We fully classify the five infinite families of pairs of ribbon Schur functions whose difference is a single Schur function with corresponding partition having at most two parts at least $2$. We also prove an identity for differences of ribbon Schur functions and we determine some necessary conditions for such a difference to be Schur-positive, depending on the distribution of $1$'s and the end row lengths.