Counting words with Laguerre series
Abstract
We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of weighted sums of Laguerre polynomials with parameter \alpha = -1. We describe how such a series can be computed by finding an appropriate ordinary generating function and applying a certain transformation. We use this technique to find the generating function for the number of k-ary words avoiding any vincular pattern that has only ones, as well as words cyclically avoiding vincular patterns with only ones whose runs of ones between dashes are all of equal length.
Cite
@article{arxiv.1306.6232,
title = {Counting words with Laguerre series},
author = {Jair Taylor},
journal= {arXiv preprint arXiv:1306.6232},
year = {2013}
}
Comments
22 pages. Submitted to the Electronic Journal of Combinatorics. An extended abstract version of this paper appears in the proceedings of FPSAC 2013 (Formal Power Series and Algebraic Combinatorics)