Statistics on integer partitions arising from seaweed algebras

TL;DR

This paper investigates new integer partition statistics derived from seaweed algebra index theory, revealing connections to classical partition varieties and uncovering a surprising periodicity phenomenon.

Contribution

It introduces novel integer partition statistics based on seaweed algebra theory and establishes new relationships and periodicity results.

Findings

Relations to classical integer partition varieties

Discovery of a surprising periodicity in partition statistics

New connections between algebraic structures and partition theory

Abstract

Using the index theory of seaweed algebras, we explore various new integer partition statistics. We find relations to some well-known varieties of integer partitions as well as a surprising periodicity result.