Some Applications Arising From The Interactions Between The Theory Of Catalan-Like Numbers And The \(ECO\) Method

Abstract

In \([FP]\) the \(ECO\) methed 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 \([SI]\).