Determinants of (generalised) Catalan numbers

We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindström–Gessel–Viennot theorem on non-intersecting lattice paths with a simple determinant lemma from Krattenthaler (1990). This approach leads also...

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Bibliographic Details
Published inJournal of statistical planning and inference Vol. 140; no. 8; pp. 2260 - 2270
Main Author Krattenthaler, C.
Format Journal Article Conference Proceeding
LanguageEnglish
Published Kidlington Elsevier B.V 01.08.2010
Elsevier
Subjects
Combinatorics. Ordered structures
Dodgson condensation
Exact sciences and technology
Fibonacci numbers
General topics
Generalised Catalan numbers
Hankel determinants
Mathematics
Non-intersecting lattice paths
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Order, lattices, ordered algebraic structures
Probability and statistics
Sciences and techniques of general use
Statistics
Non-intersecting lattice paths
Generalised Catalan numbers
Fibonacci numbers
Hankel determinants
Dodgson condensation
Statistical method
Numerical analysis
Numerical linear algebra
Determinant
Catalan number
Statistical decision
Lattice
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Summary:We show that recent determinant evaluations involving Catalan numbers and generalisations thereof have most convenient explanations by combining the Lindström–Gessel–Viennot theorem on non-intersecting lattice paths with a simple determinant lemma from Krattenthaler (1990). This approach leads also naturally to extensions and generalisations.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2010.01.022