Mixed Ehrhart polynomials
Autor(en): | Haase, Christian Juhnke-Kubitzke, Martina Sanyal, Raman Theobald, Thorsten |
Stichwörter: | (mixed) Ehrhart polynomial; discrete (mixed) volume; h*-vector; lattice polytope; Mathematics; Mathematics, Applied; real roots | Erscheinungsdatum: | 2017 | Herausgeber: | ELECTRONIC JOURNAL OF COMBINATORICS | Journal: | ELECTRONIC JOURNAL OF COMBINATORICS | Volumen: | 24 | Ausgabe: | 1 | Zusammenfassung: | For lattice polytopes P-1,...,P-k subset of R-d, Bihan (2016) introduced the discrete mixed volume DMV(P-1,...,P-k) in analogy to the classical mixed volume. In this note we study the associated mixed Ehrhart polynomial MEp(1),...,p(k)(n) = DMV(nP(1),...,nP(k)). We provide a characterization of all mixed Ehrhart coefficients in terms of the classical multivariate Ehrhart polynomial. Bihan (2016) showed that the discrete mixed volume is always non-negative. Our investigations yield simpler proofs for certain special cases. We also introduce and study the associated mixed h*-vector. We show that for large enough dilates rP(1),...,rP(k) the corresponding mixed h*-polynomial has only real roots and as a consequence the mixed h*-vector becomes non-negative. |
ISSN: | 10778926 |
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