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
2010-01-01
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.
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https://hdl.handle.net/11365/10630
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