A parallel algorithm for the enumeration of benzenoid hydrocarbons

TL;DR

This paper introduces an enhanced parallel algorithm that significantly extends the enumeration of fixed benzenoids from h=35 to h=50, providing precise estimates of their growth constant and amplitude.

Contribution

The paper presents a novel parallel algorithm that improves the enumeration range of benzenoids and confirms their asymptotic growth behavior with high accuracy.

Findings

Extended enumeration of benzenoids up to h=50

Estimated growth constant κ=5.161930154(8)

Confirmed asymptotic form of the generating function

Abstract

We present an improved parallel algorithm for the enumeration of fixed benzenoids B_h containing h hexagonal cells. We can thus extend the enumeration of B_h from the previous best h=35 up to h=50. Analysis of the associated generating function confirms to a very high degree of certainty that $B_h \sim A \kappa^h /h$ and we estimate that the growth constant $\kappa = 5.161930154(8)$ and the amplitude $A=0.2808499(1)$.