We define the notion of a Catalan pair, which is a pair of (strict) order relations (S, R) satisfying certain axioms. We show that Catalan pairs of size n are counted by Catalan numbers. We study some combinatorial properties of the relations R and S. In particular, we show that the second component R uniquely determines the pair, and we give a characterization of the poset R in terms of forbidden configurations. We also propose some generalizations of Catalan pairs arising from the modification of one of the axioms.
Disanto, F., Ferrari, L., Pinzani, R., Rinaldi, S. (2009). Combinatorial properties of Catalan pairs. ELECTRONIC NOTES IN DISCRETE MATHEMATICS, 34, 429-433 [10.1016/j.endm.2009.07.071].
Combinatorial properties of Catalan pairs
RINALDI, SIMONE
2009-01-01
Abstract
We define the notion of a Catalan pair, which is a pair of (strict) order relations (S, R) satisfying certain axioms. We show that Catalan pairs of size n are counted by Catalan numbers. We study some combinatorial properties of the relations R and S. In particular, we show that the second component R uniquely determines the pair, and we give a characterization of the poset R in terms of forbidden configurations. We also propose some generalizations of Catalan pairs arising from the modification of one of the axioms.
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https://hdl.handle.net/11365/10628
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