A new combinatorial proof confirms total positivity of the barycentric subdivision transformation matrix, proves it for interval subdivision, and gives a sufficient condition for TP2 in uniform subdivisions with an application to r-colored barycentric subdivision.
Athanasiadis,Edgewise subdivisions, localh-polynomials, and excedances in the wreath productZr ≀S n, SIAM J
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Total positivity of transformation matrices for uniform subdivisions
A new combinatorial proof confirms total positivity of the barycentric subdivision transformation matrix, proves it for interval subdivision, and gives a sufficient condition for TP2 in uniform subdivisions with an application to r-colored barycentric subdivision.