Some determinants of path generating functions
arXiv:0911.1737
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.
35 pages, AmS-TeX; minor corrections; final version to appear in Adv. Appl. Math