Super-Catalan Numbers of the Third and Fourth Kind
Irina Gheorghiciuc, Gidon Orelowitz

TL;DR
This paper investigates the combinatorial interpretations of Super-Catalan numbers for specific cases, providing solutions for m=3,4, and demonstrating the absence of solutions for m=5.
Contribution
It offers explicit combinatorial interpretations for Super-Catalan numbers when m=3,4, advancing understanding of these sequences and highlighting limitations for m=5.
Findings
Explicit combinatorial interpretations found for m=3,4
No combinatorial interpretation exists for m=5
Advances understanding of Super-Catalan numbers' combinatorial nature
Abstract
The Super-Catalan numbers are a generalization of the Catalan numbers defined as . It is an open problem to find a combinatorial interpretation for . We resolve this for using a common form; no such solution exists for .
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Coding theory and cryptography · graph theory and CDMA systems
