2022/11/20 by Bin Han, Han, Bin, Qiongqiong Pan +1
Agricultural and Biological Sciences · Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2211.10893
openalex publication_date 2022/11/20 · openalex created_date 2022/11/29 · openalex updated_date 2026/07/28
We introduce a kind of (p, q, t)-Catalan numbers of Type A by generalizing the Jacobian type continued fraction formula, we proved that the corresponding expansions could be expressed by the polynomials counting permutations on §n(321) by various descent statistics. Moreover, we introduce a kind of (p, q, t)-Catalan numbers of Type B by generalizing the Jacobian type continued fraction formula, we proved that the Taylor coefficients and their γ-coefficients could be expressed by the polynomials counting permutations on §n(3124, 4123, 3142, 4132) by various descent statistics. Our methods include permutation enumeration techniques involving variations of bijections from permutation patterns to labeled Motzkin paths and modified Foata-Strehl action.