#####
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.

The following versions are available: