Séminaire Lotharingien de Combinatoire, 85B.30 (2021), 12 pp.

Xi Chen, Bishal Deb, Alexander Dyachenko, Tomack Gilmore and Alan D. Sokal

Coefficientwise Total Positivity of Some Matrices Defined by Linear Recurrences

Abstract. We exhibit a lower-triangular matrix of polynomials T(a,c,d,e,f,g) in~six indeterminates that appears empirically to be coefficientwise totally positive, and which includes as a special case the Eulerian triangle. We prove the coefficientwise total positivity of T(a,c,0,e,0,0), which includes the reversed Stirling subset triangle.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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