Catalan structures and Catalan pairs
Copyright policy )Catalan structures and Catalan pairs
A Catalan pair is a pair of binary relations (S,R) satisfying certain axioms. These objects are enumerated by the well-known Catalan numbers, and have been introduced with the aim of giving a common language to most of the structures counted by Catalan numbers. Here, we give a simple method to pass from the recursive definition of a generic Catalan structure to the recursive definition of the Catalan pair on the same structure, thus giving an automatic way to interpret Catalan structures in terms of Catalan pairs. We apply our method to many well-known Catalan structures, focusing on the meaning of the relations S and R in each considered case.
14 pages
- New York University Italy
- University of Florence Italy
- University of Pisa Italy
- University of Siena Italy
binary relation, FOS: Computer and information sciences, Discrete Mathematics (cs.DM), representation, Binary relation; Catalan number; Catalan structures; Catalans; Common languages; Recursive definitions; SIMPLE method, Exact enumeration problems, generating functions, SIMPLE method, Catalan numbers; Catalan structures, pattern-avoiding permutation, Catalan, Combinatorics of partially ordered sets, Catalan number, pattern avoidance, poset, Binary relation, Combinatorial identities, bijective combinatorics, Permutations, words, matrices, plane tree, Common language, ordered pair, 312-avoiding permutation, Recursive definition, Catalan numbers, Catalan structure, perfect noncrossing matching, Computer Science - Discrete Mathematics
binary relation, FOS: Computer and information sciences, Discrete Mathematics (cs.DM), representation, Binary relation; Catalan number; Catalan structures; Catalans; Common languages; Recursive definitions; SIMPLE method, Exact enumeration problems, generating functions, SIMPLE method, Catalan numbers; Catalan structures, pattern-avoiding permutation, Catalan, Combinatorics of partially ordered sets, Catalan number, pattern avoidance, poset, Binary relation, Combinatorial identities, bijective combinatorics, Permutations, words, matrices, plane tree, Common language, ordered pair, 312-avoiding permutation, Recursive definition, Catalan numbers, Catalan structure, perfect noncrossing matching, Computer Science - Discrete Mathematics
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