Catalan numbers and relations
Combinatorics
2009-01-23 v1
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 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.
Cite
@article{arxiv.0901.3509,
title = {Catalan numbers and relations},
author = {Filippo Disanto and Luca Ferrari and Renzo Pinzani and Simone Rinaldi},
journal= {arXiv preprint arXiv:0901.3509},
year = {2009}
}
Comments
26 pages, 14 figures