The enumeration of independent sets on some lattices

Zuhe Zhang

Published 2008-10-06, updated 2012-09-16Version 2

In this paper, firstly we show that the entropy constants of the number of independent sets on certain plane lattices are the same as the entropy constants of the corresponding cylindrical and toroidal lattices. Secondly, we consider three more complex lattices which can not be handled by a single transfer matrix as in the plane quadratic lattice case. By introducing the concept of transfer multiplicity, we obtain the lower and upper bounds of the entropy constants of crossed quadratic lattice, generalized aztec diamond lattice and 8-8-4 lattice.