2013/07/31 by Viorel Niţică, Viorel Nitica, Sergeĭ Sergeev +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Combinatorics #Commutative Algebra and Its Applications #Convex analysis #Convex optimization #Convex polytope #Convexity #Dimension (graph theory) #Discrete mathematics #Geometry #Mathematics #Matrix (chemical analysis) #Polynomial and algebraic computation #Polytope #Pure mathematics #Rank (graph theory) #Regular polygon #Relation (database) #math.CO #math.MG #msc:15A80 #msc:16Y60 #msc:52A01
paper · pdf · doi:10.1016/j.fss.2014.10.008
published as Fuzzy Sets and Systems 271 (2015) 88-101 · 19 pages, v2: many corrections in the proofs
arxiv created 2014/01/17 · openalex publication_date 2014/10/18 · arxiv updated 2019/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We introduce a notion of dimension of max–min convex sets, following the approach of tropical convexity. We introduce a max–min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We describe the relation between this rank and the notion of strong regularity in max–min algebra, which is traditionally defined in terms of unique solvability of linear systems and the trapezoidal property.