h-Vectors of Gorenstein polytopes
DC Element | Wert | Sprache |
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dc.contributor.author | Bruns, Winfried | |
dc.contributor.author | Roemer, Tim | |
dc.date.accessioned | 2021-12-23T15:59:31Z | - |
dc.date.available | 2021-12-23T15:59:31Z | - |
dc.date.issued | 2007 | |
dc.identifier.issn | 00973165 | |
dc.identifier.uri | https://osnascholar.ub.uni-osnabrueck.de/handle/unios/3977 | - |
dc.description.abstract | We show that the Ehrhart h-vector of an integer Gorenstein polytope with a regular unimodular triangulation satisfies McMullen's g-theorem; in particular, it is unimodal. This result generalizes a recent theorem of Athanasiadis (conjectured by Stanley) for compressed polytopes. It is derived from a more general theorem on Gorenstein affine normal monoids M: one can factor K [M] (K a field) by a ``long'' regular sequence in such a way that the quotient is still a normal affine monoid algebra. This technique reduces all questions about the Ehrhart h-vector of P to the Ehrhart h-vector of a Gorenstein polytope Q with exactly one interior lattice point, provided each lattice point in a multiple cP, C is an element of N, can be written as the sum of c lattice points in P. (Up to a translation, the polytope Q belongs to the class of reflexive polytopes considered in connection with mirror symmetry.) If P has a regular unimodular triangulation, then it follows readily that the Ehrhart h-vector of P coincides with the combinatorial h-vector of the boundary complex of a simplicial polytope, and the g-theorem applies. (c) 2006 Elsevier Inc. All rights reserved. | |
dc.language.iso | en | |
dc.publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE | |
dc.relation.ispartof | JOURNAL OF COMBINATORIAL THEORY SERIES A | |
dc.subject | affine monoid | |
dc.subject | Ehrhart function | |
dc.subject | EHRHART POLYNOMIALS | |
dc.subject | Gorenstein ring | |
dc.subject | h-Vector | |
dc.subject | initial ideal | |
dc.subject | lattice polytope | |
dc.subject | Mathematics | |
dc.subject | triangulation | |
dc.subject | unimodality | |
dc.title | h-Vectors of Gorenstein polytopes | |
dc.type | journal article | |
dc.identifier.doi | 10.1016/j.jcta.2006.03.003 | |
dc.identifier.isi | ISI:000242730400005 | |
dc.description.volume | 114 | |
dc.description.issue | 1 | |
dc.description.startpage | 65 | |
dc.description.endpage | 76 | |
dc.publisher.place | 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA | |
dcterms.isPartOf.abbreviation | J. Comb. Theory Ser. A | |
dcterms.oaStatus | Green Submitted, Bronze | |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.dept | FB 06 - Mathematik/Informatik | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.deptid | fb06 | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.parentorg | Universität Osnabrück | - |
crisitem.author.netid | BrWi827 | - |
crisitem.author.netid | RoTi119 | - |
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geprüft am 10.05.2024