Catalan numbers and relations

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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.
26 pages, 14 figures

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Combinatorics, 06A07, 05A15

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http://salesiana.dossiersoluciones.com/handle/123456789/216978

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0901.3509
 http://arxiv.org/abs/0901.3509

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arXiv