A theorem on the cores of partitions

TL;DR

This paper proves that the s-core of a t-core partition remains a t-core partition when s and t are relatively prime positive integers, revealing a structural property of partition cores.

Contribution

It establishes a new theorem demonstrating the preservation of t-core property under the s-core operation for coprime integers s and t.

Findings

s-core of a t-core partition is a t-core partition

The result holds when s and t are relatively prime

Provides insight into the structure of partition cores

Abstract

If s and t are relatively prime positive integers we show that the s-core of a t-core partition is again a t-core partition