Some geometric extremal problems
نویسندگان
چکیده
منابع مشابه
Extremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric
A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...
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is achieved. This is given by e¡ = (1 -\-'Kkj)~1hj, where X is the unique positive root of £"-0 kj(l +\k])-1\hj\2 = M2. Davis proved the result by first considering the extremal problem for ra dimensional Euclidean space Rn. In this case the problem has the following geometric interpretation : (a") Let E be the hyperellipse {(oi, • • • , an): ]£?„„ kjOJ^M2} in Rn and suppose that h = (hi, • ■ ■...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1966
ISSN: 0004-9735
DOI: 10.1017/s1446788700004067