2020
DOI: 10.48550/arxiv.2008.04120
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On a Stirling-Whitney-Riordan triangle

Abstract: Motivated by the Stirling triangle of the second kind, the Whitney triangle of the second kind and a triangle of Riordan, we study a Stirling-Whitney-Riordan triangle [T n,k ] n,k satisfying the recurrence relation:where initial conditions T n,k = 0 unless 0 ≤ k ≤ n and T 0,0 = 1. Let its rowgenerating function T n (q) = k≥0 T n,k q k for n ≥ 0.We prove that the Stirling-Whitney-Riordan triangle [T n,k ] n,k is x-totally positive with x = (a 1 , a 2 , b 1 , b 2 , λ). We show real rootedness and log-concavity o… Show more

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