Tropical Convexity via Cellular Resolutions
Florian Block, Josephine Yu
TL;DR
This paper explores the structure of tropical convex hulls using cellular resolutions, enabling algebraic computation methods, and introduces tropical cyclic polytopes as a new concept.
Contribution
It establishes a connection between tropical convexity and cellular resolutions, providing a novel algebraic approach to compute tropical convex hulls and introducing tropical cyclic polytopes.
Findings
Tropical convex hulls have a cellular free resolution structure.
Methods from computational commutative algebra can compute tropical convex hulls.
Introduction of tropical cyclic polytopes.
Abstract
The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. Tropical cyclic polytopes are also presented.
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Taxonomy
TopicsPolynomial and algebraic computation · Commutative Algebra and Its Applications · Advanced Differential Equations and Dynamical Systems