2009/01/22 by Filippo Disanto, Luca Ferrari, Disanto, Filippo +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #math.CO #msc:05A15 #msc:06A07
paper · pdf · doi:10.48550/arxiv.0901.3509
26 pages, 14 figures
arxiv created 2009/01/22 · arxiv updated 2009/12/01
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.