2025/05/09 by Hanqian Fang, C. Zhang, Fang, Hanqian +2
Mathematics · #05A10 #11B83 #26C10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.2505.05873
openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Baxter numbers are known as the enumeration of Baxter permutations and numerous other discrete structures, playing a significant role across combinatorics, algebra, and analysis. In this paper, we focus on the analytic properties related to Baxter numbers. We prove that the descent polynomials of Baxter permutations have interlacing zeros, which is a property stronger than real-rootedness. Our approach is based on Dilks' framework of (q,t)-Hoggatt sums, which is a q-analog for Baxter permutations. Within this framework, we show that the family of (1,t)-Hoggatt sums satisfies the interlacing property using fundamental results on Hadamard products of polynomials. For Baxter numbers, we prove their asymptotic r-log-convexity via asymptotic expansions of P-recursive sequences. In particular, we confirm their 2-log-convexity using symbolic computation techniques.