Tropical Ehrhart theory and tropical volume

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 aris...

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Detalles Bibliográficos
Autores principales: Loho, Georg, Schymura, Matthias
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7510937/
https://www.ncbi.nlm.nih.gov/pubmed/33029581
http://dx.doi.org/10.1007/s40687-020-00228-1
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author Loho, Georg
Schymura, Matthias
author_facet Loho, Georg
Schymura, Matthias
author_sort Loho, Georg
collection PubMed
description 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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spelling pubmed-75109372020-10-05 Tropical Ehrhart theory and tropical volume Loho, Georg Schymura, Matthias Res Math Sci Research 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. Springer International Publishing 2020-09-21 2020 /pmc/articles/PMC7510937/ /pubmed/33029581 http://dx.doi.org/10.1007/s40687-020-00228-1 Text en © The Author(s) 2020 Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Research
Loho, Georg
Schymura, Matthias
Tropical Ehrhart theory and tropical volume
title Tropical Ehrhart theory and tropical volume
title_full Tropical Ehrhart theory and tropical volume
title_fullStr Tropical Ehrhart theory and tropical volume
title_full_unstemmed Tropical Ehrhart theory and tropical volume
title_short Tropical Ehrhart theory and tropical volume
title_sort tropical ehrhart theory and tropical volume
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7510937/
https://www.ncbi.nlm.nih.gov/pubmed/33029581
http://dx.doi.org/10.1007/s40687-020-00228-1
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