Combinatorics of three-Catalan numbers and some positivities

2025/02/05 by Boualam Rezig, Rezig, Boualam, Moussa Ahmia +1
Mathematics · #05A05 #05A15 #05A19 #05A30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2502.03615

openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the three-Catalan triangle, highlighting the three-Catalan numbers along with their recurrence relation and combinatorial interpretation, which allows us to establish their log-convexity. Additionally, we prove that the rows of the three-Catalan triangle form a log-concave sequence.

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