Some determinants of path generating functions, II

Abstract

We evaluate Hankel determinants of matrices in which the entries are generating functions for paths consisting of up-steps, down-steps and level steps with a fixed starting point but variable end point. By specialisation, these determinant evaluations have numerous corollaries. In particular, one consequence is that the Hankel determinant of Motzkin prefix numbers equals 1, regardless of the size of the Hankel matrix.

MSC

primary

05A19

secondary

05A10
05A15
11C20
15A15

Keywords

Hankel determinants
Catalan numbers
Ballot numbers
Motzkin numbers
Motzkin prefix numbers
Motzkin paths
1

Research partially supported by the Austrian Science Foundation FWF, grant S50-N15, in the framework of the Special Research Program “Algorithmic and Enumerative Combinatorics”.

2

Current address: Faculty of Agriculture and Animal Science, University of Torbat-e Jam, Iran.