Tropical Ehrhart theory and tropical volume

Georg Loho; Matthias Schymura

doi:10.1007/s40687-020-00228-1

Tropical Ehrhart theory and tropical volume

Georg Loho
, Matthias Schymura^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

5 Citations (Scopus)

51 Downloads (Pure)

Abstract

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

Original language	English
Article number	30
Journal	Research in Mathematical Sciences
Volume	7
Issue number	4
DOIs	https://doi.org/10.1007/s40687-020-00228-1
Publication status	Published - 1 Dec 2020
Externally published	Yes

Keywords

Ehrhart theory
Tropical geometry
Tropical lattices
Tropical polytopes
Tropical semiring
Tropical volumes

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10.1007/s40687-020-00228-1Licence: CC BY

Loho-2020-Tropical-ehrhart-theory-and-tropicaFinal published version, 971 KBLicence: CC BY

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title = "Tropical Ehrhart theory and tropical volume",

abstract = "We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.",

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author = "Georg Loho and Matthias Schymura",

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AU - Schymura, Matthias

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N2 - We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

AB - We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposition is complemented by a brief study of arising complexity questions.

KW - Ehrhart theory

KW - Tropical geometry

KW - Tropical lattices

KW - Tropical polytopes

KW - Tropical semiring

KW - Tropical volumes

UR - https://www.scopus.com/pages/publications/85091283839

U2 - 10.1007/s40687-020-00228-1

DO - 10.1007/s40687-020-00228-1

M3 - Article

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VL - 7

JO - Research in Mathematical Sciences

JF - Research in Mathematical Sciences

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Tropical Ehrhart theory and tropical volume

Abstract

Keywords

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