On Base Partitions And Cover Partitions Of Skew Characters

TL;DR

This paper provides a combinatorial method to determine base and cover partitions of skew characters, facilitating the analysis of their structure and properties in algebraic combinatorics.

Contribution

It introduces an easy combinatorial description for the base partition of skew characters and constructs cover partitions for various character products, including Schubert products.

Findings

Derived the base partition as an intersection of partitions.

Constructed cover partitions as unions of partitions in products.

Determined Durfee size for arbitrary Schubert products.

Abstract

In this paper we give an easy combinatorial description for the base partition B of a skew character [A], which is the intersection of all partitions alpha whose corresponding character [alpha] appears in [A]. This we use to construct the cover partition C for the ordinary outer product as well as for the Schubert product of two characters and for some skew characters, here the cover partition is the union of all partitions whose corresponding character appears in the product or in the skew character. This gives us also the Durfee size for arbitrary Schubert products.