A noncommutative enumeration problem

TL;DR

This paper explores the combinatorics of coloured hard-dimer objects by representing them as rooted trees and analyzing them using noncommutative formal power series, providing an algebraic approach to their enumeration.

Contribution

It introduces a novel algebraic framework for enumerating coloured hard-dimer configurations through noncommutative formal power series.

Findings

Established a correspondence between coloured hard-dimer configurations and rooted trees.

Developed an algebraic method for counting these configurations.

Provided new tools for combinatorial enumeration using noncommutative algebra.

Abstract

In this article we tackle the combinatorics of coloured hard-dimer objects. This is achieved by identifying coloured hard-dimer configurations with a certain class of rooted trees that allow for an algebraic treatment in terms of noncommutative formal power series.