Catalan states of lattice crossing: An application of plucking polynomial

摘要

For a Catalan state C of a lattice crossing L (m, n) with no returns on one side, we find its coefficient C (A) in the Relative Kauffman Bracket Skein Module expansion of L (m, n). We show, in particular, that C (A) can be found using the plucking polynomial of a rooted tree with a delay function associated to C. Furthermore, for C with returns on one side only, we prove that C (A) is a product of Gaussian polynomials, and its coefficients form a unimodal sequence. Published by Elsevier B.V.