Counting Abelian Squares

TL;DR

This paper counts the number of abelian squares, a special class of strings, and provides an asymptotic estimate for their quantity, advancing understanding of their combinatorial properties.

Contribution

It introduces a method to count abelian squares and derives an asymptotic estimate, offering new insights into their enumeration.

Findings

Derived an explicit count of abelian squares

Provided an asymptotic estimate for large string lengths

Enhanced understanding of the combinatorial structure of abelian squares

Abstract

An abelian square is a string of length 2n where the last n symbols form a permutation of the first n symbols. In this note we count the number of abelian squares and give an asymptotic estimate of this quantity.