Analytic aspects of generalized central trinomial coefficients

2023/03/13 by Liang, Huyile, Wang, Yaling, Wang, Yi · 1 citation
#05A15 #15B48 #26C10 #60F0 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.06922

Abstract

The divisibility and congruence of usual and generalized central trinomial coefficients have been extensively investigated. The present paper is devoted to analytic properties of these numbers. We show that usual central trinomial polynomials T_n(x) have only real roots, and roots of T_n(x) interlace those of T_n+1(x), as well as those of T_n+2(x), which gives an affirmative answer to a open question of Fisk. We establish necessary and sufficient conditions such that the generalized central trinomial coefficients T_n(b,c) form a log-convex sequence or a Stieltjes moment sequence.

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