Tropical Ehrhart Theory and Tropical Volume
Georg Loho, Matthias Schymura
TL;DR
This paper develops a new intrinsic volume concept in tropical geometry, establishing a tropical analog of lattice point counting in polytopes and exploring its properties and complexity aspects.
Contribution
Introduces a novel intrinsic volume in tropical geometry and develops foundational tools for tropical lattice point counting.
Findings
Defined basic properties of the tropical intrinsic volume
Compared the new measure to existing geometric measures
Explored complexity questions related to tropical lattice counting
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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