The Number of Independent Sets in Hexagonal Graphs

A new method is proposed to derive rigorous bounds on {\eta}, the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. Specifically, we prove that 1.546440708536001 <= {\eta} <= 1.5513, which improves upon the best known 1.5463 <= {\eta} <= 1.5527 due to Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point.