Some stable plethysms

TL;DR

This paper establishes new stability results for plethysm coefficients, confirming conjectures and predictions about their behavior, which advances understanding in algebraic combinatorics and representation theory.

Contribution

It proves new stability theorems for plethysm coefficients, verifying a conjecture of Wildon and confirming recent predictions by Bessenrodt, Bowman, and Paget.

Findings

Verified Wildon's conjecture on plethysm stability

Demonstrated stability of certain weakly increasing sequences

Extended understanding of plethysm coefficient behavior

Abstract

In this note, we prove some new stability results for plethysm coefficients. As special cases, we verify a conjecture of Wildon, and show the stability of sequences recently predicted by Bessenrodt, Bowman and Paget to be weakly increasing.