The number of independent sets in hexagonal graphs

Conference Paper

We derive the tightest known bounds on η = 2ν, where ν is the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. To obtain these bounds, we generalize a method proposed by Calkin and Wilf. Their original strategy cannot immediately be used to derive bounds for η, due to the difference in symmetry between square and hexagonal lattices, so we propose a modified method and an algorithm to derive rigorous bounds on η. In particular, we prove that 1.546440708536001 ≤ η ≤ 1.5513, which improves upon the best known bounds of 1.5463 ≤ η ≤ 1.5527 given by Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point, and our upper bound can be further improved by following our method.

Full Text

Duke Authors

Cited Authors

  • Deng, Z; Ding, J; Heal, K; Tarokh, V

Published Date

  • August 9, 2017

Published In

Start / End Page

  • 2910 - 2914

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781509040964

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2017.8007062

Citation Source

  • Scopus