Catalan numbers and relations

Details Catalan numbers and relations Catalan numbers and relations

2009-01-22

arxiv.org/abs/0901.3509v1

Mathematics

Combinatorics

26 pages, 14 figures

Scientific paper

We define the notion of a Catalan pair (which is a pair of binary relations (S,R) satisfying certain axioms) with the aim of giving a common language to most of the combinatorial interpretations of Catalan numbers. We show, in particular, that the second component R uniquely determines the pair, and we give a characterization of R in terms of forbidden configurations. We also propose some generalizations of Catalan pairs arising from some slight modifications of (some of the) axioms.

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