In [FP] the ECO method and Aigner's theory of Catalan-like numbers are compared, showing that it is often possible to translate a combinatorial situation from one theory into the other by means of a standard change of basis in a suitable vector space. In the present work we emphasize the soundness of such an approach by finding some applications suggested by the above mentioned translation. More precisely, we describe a presumably new bijection between two classes of lattice paths and we give a combinatorial interpretation to an integer sequence not appearing in [S1].
Ferrari, L., Pergola, E., Pinzani, R., Rinaldi, S. (2011). Some applications arising from the interactions between the theory of Catalan-like numbers and the ECO method. ARS COMBINATORIA, 99, 109-128.
Some applications arising from the interactions between the theory of Catalan-like numbers and the ECO method
RINALDI, SIMONE
2011-01-01
Abstract
In [FP] the ECO method and Aigner's theory of Catalan-like numbers are compared, showing that it is often possible to translate a combinatorial situation from one theory into the other by means of a standard change of basis in a suitable vector space. In the present work we emphasize the soundness of such an approach by finding some applications suggested by the above mentioned translation. More precisely, we describe a presumably new bijection between two classes of lattice paths and we give a combinatorial interpretation to an integer sequence not appearing in [S1].
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https://hdl.handle.net/11365/26314
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