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 several 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.

Disanto, F., Ferrari, L., Pinzani, R., & Rinaldi, S. (2010). Catalan relations: a relational-theoretic approach to Catalan numbers. ADVANCES IN APPLIED MATHEMATICS, 45, 505-517.

Catalan relations: a relational-theoretic approach to Catalan numbers

RINALDI, SIMONE
2010

Abstract

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 several 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.
Disanto, F., Ferrari, L., Pinzani, R., & Rinaldi, S. (2010). Catalan relations: a relational-theoretic approach to Catalan numbers. ADVANCES IN APPLIED MATHEMATICS, 45, 505-517.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11365/10630
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