Geodesic
Proof of Chapoton's conjecture on Newton polygons of \(q\)-Ehrhart polynomials
The electronic journal of combinatorics, Tome 25 (2018) no. 2
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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.
DOI : 10.37236/7322
Classification : 05A30, 52B20, 06A07
Mots-clés : \(q\)-Ehrhart polynomial, Newton polytope, order polytope, \(P\)-partition 
@article{10_37236_7322,
     author = {Jang Soo Kim and U-Keun Song},
     title = {Proof of {Chapoton's} conjecture on {Newton} polygons of {\(q\)-Ehrhart} polynomials},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {2},
     doi = {10.37236/7322},
     zbl = {1452.05009},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7322/}
}
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Jang Soo Kim; U-Keun Song. Proof of Chapoton's conjecture on Newton polygons of \(q\)-Ehrhart polynomials. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/7322

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