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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
##### Keywords:
Catalan numbers; parking functions; inversions; permutations
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