zbMATH — the first resource for mathematics

A left weighted Catalan extension. (English) Zbl 1226.05011
Summary: There are many representations of the Catalan numbers. In this article, we will examine the ballot problem and extend it beyond the standard \(p\)-Catalan extension to a left weighted extension. This extension reduces naturally to the \(p\)-Catalan numbers (including the standard 2-Catalan numbers). We will then give a variety of examples of the extension for other representations of the Catalan numbers to demonstrate its general applicability.

05A05 Permutations, words, matrices
05A17 Combinatorial aspects of partitions of integers
05A18 Partitions of sets
05A15 Exact enumeration problems, generating functions
Full Text: DOI EuDML