Exact dimer statistics and characteristic polynomials of cacti lattices

Summary The pruning method developed earlier by one of the authors (K.B.) combined with the operator method is shown to yield powerful recursive relations for generating functions for dimer statistics and characteristic polynomials of cacti graphs and cacti lattices. The method developed is applied to linear cacti, Bethe cacti of any length containing rings of any size, and cyclic cacti of any length and size. It is shown that exact dimer statistics can be done on any cactus lattice.Dedicated to Professor V. Krishnamurthy on the occasion of his 60th birthdayAlfred P. Sloan fellow; Camille and Henry Dreyfus teacher-scholar