A Catalan pair is a pair of binary relations (S,R) satisfying some axioms. These pairs are enumerated by the well-known Catalan numbers, and have been introduced in Disanto et al. (2010) [2] with the aim of giving a common language to many structures counted by Catalan numbers. Here, a simple method is given 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 of interpreting Catalan structures in terms of Catalan pairs. Our method is applied to several well-known Catalan structures, focusing on the combinatorial meaning of the relations S and R in each case considered

Bilotta, S., Disanto, F., Pinzani, R., Rinaldi, S. (2013). Catalan structures and Catalan pairs. THEORETICAL COMPUTER SCIENCE, 502(2), 239-248 [10.1016/j.tcs.2012.07.007].

Catalan structures and Catalan pairs

DISANTO, FILIPPO;RINALDI, SIMONE
2013-01-01

Abstract

A Catalan pair is a pair of binary relations (S,R) satisfying some axioms. These pairs are enumerated by the well-known Catalan numbers, and have been introduced in Disanto et al. (2010) [2] with the aim of giving a common language to many structures counted by Catalan numbers. Here, a simple method is given 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 of interpreting Catalan structures in terms of Catalan pairs. Our method is applied to several well-known Catalan structures, focusing on the combinatorial meaning of the relations S and R in each case considered
Bilotta, S., Disanto, F., Pinzani, R., Rinaldi, S. (2013). Catalan structures and Catalan pairs. THEORETICAL COMPUTER SCIENCE, 502(2), 239-248 [10.1016/j.tcs.2012.07.007].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11365/46103
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