Some determinants of path generating functions
Combinatorics
2011-04-20 v3
Abstract
We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By specialisation, these determinant evaluations have numerous corollaries. In particular, they cover numerous determinant evaluations of combinatorial numbers - most notably of Catalan, ballot, and of Motzkin numbers - that appeared previously in the literature.
Keywords
Cite
@article{arxiv.0911.1737,
title = {Some determinants of path generating functions},
author = {Christian Krattenthaler and Johann Cigler},
journal= {arXiv preprint arXiv:0911.1737},
year = {2011}
}
Comments
35 pages, AmS-TeX; minor corrections; final version to appear in Adv. Appl. Math