The p7 term in the new Expansion for Lambda2(p) of the Monomer-Dimer Problem

TL;DR

This paper extends the power series expansion of Lambda_d(p) for the monomer-dimer problem to the seventh term in two dimensions, utilizing a new algorithm for computing the Tutte polynomial.

Contribution

It introduces the seventh term in the expansion of Lambda_d(p) for d=2, enabled by a novel algorithm for Tutte polynomial computation.

Findings

Successfully computed the seventh term in the series for d=2.

Demonstrated the application of a new Tutte polynomial algorithm.

Extended previous series results up to the seventh order.

Abstract

In a recent paper S. Friedland and the author presented a formal expression for Lambda_d(p) of the monomer-dimer problem in d dimensions involving a power series in p. We there presented the result of computations for the terms in the power series through the sixth power. I herein present the result for the seventh power term, in d = 2. An interesting feature of the new computation is that it would have been impossible without a new algorithm for computation of the Tutte polynomial, by Bjorklund, Husfeldt, Kaski, and Koivisto.