Real-rooted Ehrhart h^*-polynomials of crown posets and wheel and whirl matroids

This is the authors' abstract. We don't add key points for this paper.

We prove that the Ehrhart h^*-polynomials of crown order polytopes are real-rooted, settling a conjecture of Lundström and Saud Maia Leite. For each integer r≥3, the crown order polytope on $2r$ elements and the rank-r whirl base polytope have the same h^*-polynomial. The h^*-polynomials of the rank-r wheel and whirl base polytopes, as well as every convex combination of the two, have $2r-2$ distinct negative roots. Their coefficient sequences are positive, unimodal, and strictly ultra log-concave of order $2r-2$.