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The tropical
semiring in higher dimensions
John Norton and Sandra Spiroff
Vol. 11 (2018), No. 3, 477–488
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Abstract |
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We discuss the generalization, in higher dimensions, of the tropical semiring, whose two binary operations on the set of real numbers together with infinity are defined to be the minimum and the sum of a pair, respectively. In particular, our objects are closed convex sets, and for any pair, we take the convex hull of their union and their Minkowski sum, respectively, as the binary operations. We consider the semiring in several different cases, determined by a recession cone. |
Keywords
tropical semiring, polyhedra, compact subsets
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Mathematical Subject Classification 2010
Primary: 16Y60, 52B11, 52A20
Secondary: 52A07
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Milestones
Received: 8 December 2016
Revised: 26 May 2017
Accepted: 13 June 2017
Published: 20 October 2017
Communicated by Scott T. Chapman
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Authors |
| John Norton | |
| Department of Mathematics University of Mississippi University, MS United States |
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| Sandra Spiroff | |
| Department of Mathematics University of Mississippi University, MS United States |
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