On the equivalence problem for succession rules

摘要: The notion of succession rule (system for short) provides a powerful tool the enumeration many classes combinatorial objects. Often, different systems exist given class objects, and number problems arise naturally. An important one is equivalence problem between two systems. In this paper, we show how to solve in case having particular form. More precisely, using bijective proof, that classical system defining sequence Catalan numbers equivalent obtained by linear combinations labels first one.