We introduce a notion of dimension of maxââ?¬â??min convex sets, following the approach of tropical convexity. We introduce a\nmaxââ?¬â??min analogue of the tropical rank of a matrix and show that it is equal to the dimension of the associated polytope. We\ndescribe the relation between this rank and the notion of strong regularity in maxââ?¬â??min algebra, which is traditionally defined in\nterms of unique solvability of linear systems and the trapezoidal property.
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