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Title: The mixed degree of families of lattice polytopes
Author(s): Nill, Benjamin
Issue Date: 2020
Type: Article
Language: English
URN: urn:nbn:de:gbv:ma9:1-1981185920-621971
Subjects: Mixed degree
Mixed volume
Ehrhart polynomials
Lattice polytopes
Abstract: The degree of a lattice polytope is a notion in Ehrhart theory that was studied quite intensively over previous years. It is well known that a lattice polytope has normalized volume one if and only if its degree is zero. Recently, Esterov and Gusev gave a complete classification result for families of n lattice polytopes in Rn whose mixed volume equals one. Here, we give a reformulation of their result involving the novel notion of mixed degree that generalizes the degree similar to how the mixed volume generalizes the volume. We discuss and motivate this terminology, also from an algebro-geometric viewpoint, and explain why it extends a previous definition of Soprunov. We also remark how a recent combinatorial result due to Bihan solves a related problem posed by Soprunov.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Projekt DEAL 2020
Journal Title: Annals of combinatorics
Publisher: [Springer International Publishing AG]
Publisher Place: [Cham (ZG)]
Volume: 24
Original Publication: 10.1007/s00026-019-00490-3
Page Start: 203
Page End: 216
Appears in Collections:Fakultät für Mathematik (OA)

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