On super Catalan polynomials

2014/03/20 by Emily Allen, Allen, Emily, Irina Gheorghiciuc +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1403.5296

10 pages, 4 figures

openalex publication_date 2014/03/20 · arxiv created 2014/08/31 · arxiv updated 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a q-analog of the super Catalan number (2m)!(2n)!/2m!n!(m+n)!, which also generalizes the q-Catalan numbers c_n(λ), due to Fürlinger and Hofbauer, for λ=0 and λ=1. We give a combinatorial interpretation for this analog when m=2.

Related

• Super-Catalan Numbers of the Third and Fourth Kind
• A weighted interpretation for the super Catalan numbers
• Super FiboCatalan Numbers and their Lucas Analogues
• Some observations about super Catalan numbers, corresponding orthogonal polynomials, and their q-analogues
• q-Super Catalan Numbers: Combinatorial identities, Generating Functions, and Narayana Refinements