Geodesic
Asymmetric tropical distances and power diagrams
Comăneci, Andrei1 ; Joswig, Michael2
1 Technische Universität Berlin, Chair of Discrete Mathematics/Geometry
2 Technische Universität Berlin, Chair of Discrete Mathematics/Geometry Max-Planck Institute for Mathematics in the Sciences, Leipzig
Algebraic Combinatorics, Tome 6 (2023) no. 5, pp. 1211-1233

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We investigate Voronoi diagrams with respect to an asymmetric tropical distance function, in particular for infinite point sets. These Voronoi diagrams turn out to be much better behaved than those arising from the standard tropical distance, which is symmetric. In particular, we show that the asymmetric tropical Voronoi diagrams may be seen as tropicalizations of power diagrams over fields of real Puiseux series. Our results are then applied to rational lattices and Laurent monomial modules.

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DOI : 10.5802/alco.306
Classification : 14T15, 13D02, 46B20, 52B55
Keywords: tropical convexity, polyhedral combinatorics, polyhedral gauge, ordinary and tropical quasi-polyhedron, rational lattice, Delone complex, monomial ideal, Scarf complex

Comăneci, Andrei 1 ; Joswig, Michael 2

1 Technische Universität Berlin, Chair of Discrete Mathematics/Geometry
2 Technische Universität Berlin, Chair of Discrete Mathematics/Geometry Max-Planck Institute for Mathematics in the Sciences, Leipzig
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Comăneci, Andrei; Joswig, Michael. Asymmetric tropical distances and power diagrams. Algebraic Combinatorics, Tome 6 (2023) no. 5, pp. 1211-1233. doi: 10.5802/alco.306

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