Determinants of (generalised) Catalan numbers

Details Determinants of (generalised) Catalan numbers Determinants of (generalised) Catalan numbers

2007-09-19

arxiv.org/abs/0709.3044v2

J. Statist. Plann. Inference 140 (2010), 2260-2270

Mathematics

Combinatorics

AmS-TeX, 16 pages; minor corrections

Scientific paper

We show that recent determinant evaluations involving Catalan numbers and
generalisations thereof have most convenient explanations by combining the
Lindstr\"om-Gessel-Viennot theorem on non-intersecting lattice paths with a
simple determinant lemma from [Manuscripta Math. 69 (1990), 173-202]. This
approach leads also naturally to extensions and generalisations.

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