Citation link:
https://doi.org/10.26092/elib/1559
Ehrhart Quasi-Polynomials of almost integral polytopes
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thesis_publication.pdf | Ehrhart Quasi-Polynomials of Almost Integral Polytopes | 495.42 kB | Adobe PDF | View/Open |
Authors: | de Vries, Christopher ![]() |
Supervisor: | Feichtner, Eva-Maria ![]() |
1. Expert: | Feichtner, Eva-Maria ![]() |
Experts: | Yoshinaga, Masahiko ![]() |
Abstract: | In this thesis we characterize centrally symmetric lattice polytopes and lattice zonotopes through properties of the Ehrhart quasi-polynomials of almost integral polytopes. To this end, we introduce the notion of GCD-property and symmetry for quasi-polynomials. A lattice polytope is centrally symmetric if and only if the Ehrhart quasi-polynomial of every almost integral polytope derived from that ... In this thesis we characterize centrally symmetric lattice polytopes and lattice zonotopes through properties of the Ehrhart quasi-polynomials of almost integral polytopes. To this end, we introduce the notion of GCD-property and symmetry for quasi-polynomials. A lattice polytope is centrally symmetric if and only if the Ehrhart quasi-polynomial of every almost integral polytope derived from that polytope is symmetric. Furthermore, we show that a lattice polytope is a zonotope if and only if the Ehrhart quasi-polynomial of every almost integral polytope derived from that polytope satisfies the GCD-property. In order to describe the constituents of the Ehrhart quasi-polynomial of an almost integral polytope, we introduce the translated lattice point enumerator and prove that this function is a polynomial. |
Keywords: | Polytopes; Ehrhart Theory |
Issue Date: | 17-May-2022 |
Type: | Dissertation |
Secondary publication: | no |
DOI: | 10.26092/elib/1559 |
URN: | urn:nbn:de:gbv:46-elib59546 |
Institution: | Universität Bremen |
Faculty: | Fachbereich 03: Mathematik/Informatik (FB 03) |
Appears in Collections: | Dissertationen |
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