Vol. 11, No. 3, 2018

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The tropical semiring in higher dimensions

John Norton and Sandra Spiroff

Vol. 11 (2018), No. 3, 477–488

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.

tropical semiring, polyhedra, compact subsets
Mathematical Subject Classification 2010
Primary: 16Y60, 52B11, 52A20
Secondary: 52A07
Received: 8 December 2016
Revised: 26 May 2017
Accepted: 13 June 2017
Published: 20 October 2017

Communicated by Scott T. Chapman
John Norton
Department of Mathematics
University of Mississippi
University, MS
United States
Sandra Spiroff
Department of Mathematics
University of Mississippi
University, MS
United States