Extremal problems for finite sets and convex hulls — A survey
نویسندگان
چکیده
منابع مشابه
Extremal Problems on Finite Sets and Posets
The overarching theme of the thesis is the investigation of extremal problems involving forbidden partially ordered sets (posets). In particular, we will be concerned with the function La(n, P ), defined to be the maximum number of sets we can take in the Boolean lattice 2[n] without introducing the relations of a poset P as containment relations among the sets. This function plays an analogous...
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Consider a convex polygon Vn with n sides, perimeter Pn, diameter Dn, area An, sum of distances between vertices Sn and widthWn. Minimizing or maximizing any of these quantities while fixing another defines ten pairs of extremal polygon problems (one of which usually has a trivial solution or no solution at all). We survey research on these problems, which uses geometrical reasoning increasingl...
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Given a hypergraph H and a subset S of its vertices, the trace of H on S is defined as H|S = {E ∩ S : E ∈ H}. The Vapnik–Chervonenkis dimension (VC-dimension) of H is the size of the largest subset S for which H|S has 2|S| edges. Hypergraphs of small VC-dimension play a central role in many areas of statistics, discrete and computational geometry, and learning theory. We survey some of the most...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00050-7