Chow and augmented Chow polynomials of finite graded simplicial posets with nonnegative h-vectors, including Cohen-Macaulay simplicial posets, are real-rooted, with an interlacing result for duals.
Athanasiadis and Katerina Kalampogia-Evangelinou, Chain enumeration, partition lattices and polynomials with only real roots, Comb
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Chow polynomials of simplicial posets with positive $h$-vector are real-rooted
Chow and augmented Chow polynomials of finite graded simplicial posets with nonnegative h-vectors, including Cohen-Macaulay simplicial posets, are real-rooted, with an interlacing result for duals.