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.

Catalan structures and Catalan pairs / S. Bilotta; F. Disanto; R. Pinzani; S. Rinaldi. - ELETTRONICO. - (2010), pp. 1-14. (Intervento presentato al convegno GASCom 2010 tenutosi a Montreal, Canada nel 02/09/2010 - 04/09/2010).

Catalan structures and Catalan pairs

BILOTTA, STEFANO;PINZANI, RENZO;
2010

Abstract

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.
2010
Atti locali di congresso
GASCom 2010
Montreal, Canada
02/09/2010 - 04/09/2010
S. Bilotta; F. Disanto; R. Pinzani; S. Rinaldi
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/558291
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