منابع مشابه
On Sumsets and Convex Hull
One classical result of Freiman gives the optimal lower bound for the cardinality of A + A if A is a d-dimensional finite set in R. Matolcsi and Ruzsa have recently generalized this lower bound to |A+ kB| if B is d-dimensional, and A is contained in the convex hull of B. We characterize the equality case of the Matolcsi–Ruzsa bound. The argument is based partially on understanding triangulation...
متن کاملSumsets and the Convex Hull
We extend Freiman's inequality on the cardinality of the sumset of a d dimensional set. We consider different sets related by an inclusion of their convex hull, and one of them added possibly several times.
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This is a survey on tropical polytopes from the combinatorial point of view and with a focus on algorithms. Tropical convexity is interesting because it relates a number of combinatorial concepts including ordinary convexity, monomial ideals, subdivisions of products of simplices, matroid theory, finite metric spaces, and the tropical Grassmannians. The relationship between these topics is expl...
متن کاملConvex Hull Computations
The “convex hull problem” is a catch-all phrase for computing various descriptions of a polytope that is either specified as the convex hull of a finite point set in R or as the intersection of a finite number of halfspaces. We first define the various problems and discuss their mutual relationships (Section 26.1). We discuss the very special case of the irredundancy problem in Section 26.2. We...
متن کاملDigital convex fuzzy hull
Problem of defining convexity of a digital region is considered. Definition of DL− (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T−(triangle) convexity and L−(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced...
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ژورنال
عنوان ژورنال: Topological Methods in Nonlinear Analysis
سال: 2017
ISSN: 1230-3429
DOI: 10.12775/tmna.2016.089