Congruences on sums of super Catalan numbers
Ji-Cai Liu
TL;DR
This paper proves two new congruences involving double sums of super Catalan numbers, confirming recent conjectures and advancing understanding of their arithmetic properties.
Contribution
It establishes two proven congruences on sums of super Catalan numbers, addressing conjectures by Apagodu and expanding knowledge in combinatorial number theory.
Findings
Proved two congruences on double sums of super Catalan numbers.
Confirmed conjectures proposed by Apagodu.
Enhanced understanding of super Catalan number properties.
Abstract
In this paper, we prove two congruences on the double sums of the super Catalan numbers (named by Gessel), which were recently conjectured by Apagodu.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Mathematical Identities · Analytic Number Theory Research