Asymptotic Expansions for lambda_d of the Dimer and Monomer-Dimer Problems

TL;DR

This paper presents a collection of asymptotic expansions for lambda_d in the dimer and monomer-dimer problems, highlighting results in two dimensions inspired by Fisher's work, with contributions from Friedland.

Contribution

It compiles and analyzes asymptotic expansions for lambda_d and lambda_d(p), providing new insights especially in two-dimensional cases.

Findings

Collected numerous asymptotic expansions for lambda_d and lambda_d(p)

Provided new results in two-dimensional cases inspired by Fisher

Joint work with Friedland enhances the understanding of these problems

Abstract

In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two dimensions inspired by the work of M. E. Fisher. Much of the work reported here was joint with Shmuel Friedland.