Year: 2025
Type: article
Abstract: The generalized second-order central trinomial coefficients Tn(2)(b,c) are a special case of the generalized r-order central trinomial coefficients, corresponding to r=2. We show that all zeros of the polynomial T(2)n(x)=∑k=0⌊n/2⌋T(2)(n,k)xk are real. And zeros of T(2)n−1(x) interlace those of T(2)n−2(x), as well as those of T(2)n(x). Using this result, we also discuss the asymptotic normality of T(2)(n,k).
Source: Mathematics
DOI: 10.3390/math13091430
Authors: Yu-Yang Zhang, Hao Pan, Lei Chen
Institution: Nanjing University of Finance and Economics
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4409896624