Tropical Convexity via Cellular Resolutions
نویسندگان
چکیده
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. This approach is computationally competitive with combinatorial methods. Tropical cyclic polytopes are also presented.
منابع مشابه
Tropical Types and Associated Cellular Resolutions
An arrangement of finitely many tropical hyperplanes in the tropical torus T leads to a notion of ‘type’ data for points in T, with the underlying unlabeled arrangement giving rise to ‘coarse type’. It is shown that the decomposition of T induced by types gives rise to minimal cocellular resolutions of certain associated monomial ideals. Via the Cayley trick from geometric combinatorics this al...
متن کاملCloud field segmentation via multiscale convexity analysis
[1] Cloud fields retrieved from remotely sensed satellite data resemble functions depicting spectral values at each spatial position (x,y). Segmenting such cloud fields through a simple thresholding technique may not provide any structurally significant information about each segmented category. An approach based on the use of multiscale convexity analysis to derive structurally significant reg...
متن کاملTropical Convex Hull Computations
This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial ideals, subdivisions of products of simplices, matroid theory, finite metric spaces, and the tropical Grassmannians. The relationship between these topics is expl...
متن کاملTropical Polytopes and Cellular Resolutions
Tropical polytopes are images of polytopes in an affine space over the Puiseux series field under the degree map. This viewpoint gives rise to a family of cellular resolutions of monomial ideals which generalize the hull complex of Bayer and Sturmfels [1], instances of which improve upon the hull resolution in the sense of being smaller. We also suggest a new definition of a face of a tropical ...
متن کاملTropical Convexity
The notions of convexity and convex polytopes are introduced in the setting of tropical geometry. Combinatorial types of tropical polytopes are shown to be in bijection with regular triangulations of products of two simplices. Applications to phylogenetic trees are discussed.
متن کامل