Convergence of the Formal Expansion for lambda_d(p) of the Monomer-Dimer Problem for Small p

TL;DR

This paper proves that a formal expansion for lambda_d(p) in the monomer-dimer problem converges as a power series in p when p is sufficiently small, confirming the validity of the expansion.

Contribution

It demonstrates the convergence of the formal expansion for lambda_d(p) in the monomer-dimer problem for small p, providing a rigorous foundation for the series.

Findings

The power series expansion converges for sufficiently small p.

The formal expansion for lambda_d(p) is validated as a convergent series.

Provides a rigorous proof of convergence for the expansion.

Abstract

Shmuel Friedland and the author recently presented a formal expansion for lambda_d(p) of the monomer-dimer problem. Herein we prove that if the terms in the expansion are rearranged as a power series in p, then for sufficiently small p this series converges.