A determinant representation for generalized ballot and Fuss-Catalan numbers
Combinatorics
2013-12-12 v1
Abstract
In this note we introduce a determinant and then give its evaluating formula. The determinant turns out to be a generalization of the well-known ballot and Fuss-Catalan numbers, which is believed to be new. The evaluating formula is proved by showing that the determinant coincides with the number of lattice paths with (1,0), (0,1)-steps in the plane that stay below a boundary line of rational slope.
Keywords
Cite
@article{arxiv.1312.3164,
title = {A determinant representation for generalized ballot and Fuss-Catalan numbers},
author = {James J. Y. Zhao},
journal= {arXiv preprint arXiv:1312.3164},
year = {2013}
}