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Séminaire Lotharingien de Combinatoire, 80B.27 (2018), 12 pp.

# Jang Soo
Kim and U-Keun
Song

# Proof of Chapoton's cCnjecture on Newton Polygons of *q*-Ehrhart
polynomials

**Abstract.**
Recently, Chapoton found a *q*-analog of Ehrhart polynomials, which
are polynomials in *x* whose coefficients are rational functions in
*q*.
Chapoton conjectured the shape of the Newton polygon of the numerator
of the *q*-Ehrhart polynomial of an order polytope. In this paper, we
prove Chapoton's conjecture.

Received: November 14, 2017.
Accepted: February 17, 2018.
Final version: April 1, 2018.

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