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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.

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