Counting Abelian Squares More Efficiently

TL;DR

This paper introduces a recursive formula for efficiently counting abelian squares over a given alphabet, significantly reducing computational complexity especially for large alphabet sizes.

Contribution

The paper presents a new recursive formula for counting abelian squares that is more efficient than previous methods when the alphabet size is large.

Findings

Recursive formula reduces computational complexity for large alphabets.

Significantly faster counting of abelian squares in certain cases.

Potential applications in combinatorics and string analysis.

Abstract

I present a recursive formula for calculating the number of abelian squares of length $n+n$ over an alphabet of size $d$. The presented formula is similar to a previously known formula but has substantially lower complexity when $d\gg n$.