Tropical Ehrhart Theory and Tropical Volume

Loho, Georg; Schymura, Matthias

doi:10.48550/arxiv.1908.07893

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In recent work, Loho and Schymura [LS19] developed a notion of volume for tropical polytopes driven by a tropical version of dilation, which yields an Ehrhart theory for a new class of tropical lattices. This notion of volume is intrinsically tropical and exhibits many natural properties of a volume measure, such as being monotonic and rotation-invariant.…”

Section: Introductionmentioning

confidence: 99%

Multivariate volume, Ehrhart, and $h^*$-polynomials of polytropes

Brandenburg¹,

Sophia²,

Leon³

2020

Preprint

View full text Add to dashboard Cite

The univariate Ehrhart and h * -polynomials of lattice polytopes have been widely studied. We describe methods from toric geometry for computing multivariate versions of volume, Ehrhart and h * -polynomials of lattice polytropes, which are both tropically and classically convex. These algorithms are applied to all polytropes of dimensions 2, 3 and 4, yielding a large class of integer polynomials. We give a complete combinatorial description of the coefficients of volume polynomials of 3-dimensional polytropes in terms of regular central subdivisions of the fundamental polytope. Finally, we provide a partial characterization of the analogous coefficients in dimension 4.

show abstract

Section: Introductionmentioning

confidence: 99%