Tropical Ehrhart theory and tropical volume-Reference-Cited by-同舟云学术

Tropical Ehrhart theory and tropical volume

Published:2020-09-21 Issue:4 Volume:7 Page:
ISSN:2522-0144
Container-title:Research in the Mathematical Sciences
language:en
Short-container-title:Res Math Sci

Author:

Loho Georg,Schymura Matthias^ORCID

Abstract

AbstractWe 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.

Funder

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung

H2020 European Research Council

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Mathematics (miscellaneous),Theoretical Computer Science

Link

https://link.springer.com/content/pdf/10.1007/s40687-020-00228-1.pdf

Reference38 articles.

1. Akian, M.: Densities of idempotent measures and large deviations. Trans. Am. Math. Soc. 351(11), 4515–4543 (1999)

2. Allamigeon, X., Benchimol, P., Gaubert, S., Joswig, M.: Log-barrier interior point methods are not strongly polynomial. SIAM J. Appl. Algebra Geom. 2(1), 140–178 (2018)

3. Allamigeon, X., Katz, R.D.: Minimal external representations of tropical polyhedra. J. Combin. Theory Ser. A 120(4), 907–940 (2013)

4. Allamigeon, X., Katz, R.D.: Tropicalization of facets of polytopes. Linear Algebra Appl. 523, 79–101 (2017)

5. Baldoni, V., Berline, N., De Loera, J.A., Köppe, M., Vergne, M.: Computation of the highest coefficients of weighted Ehrhart quasi-polynomials of rational polyhedra. Found. Comput. Math. 12(4), 435–469 (2012)

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