منابع مشابه
Determining sets
We give several constructions of determining sets in various settings. We also demonstrate the connections between determining sets, skew karcs and linear codes of minimum distance 5. 1. Motivation. Let P be a non-empty set of elements which we shall call points. Let B be a non-empty set of subsets of P which we shall call blocks. We consider the use of a point/block system S = (P, B) in a mess...
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A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show th...
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In 1960, Klee showed that a subset of a Euclidean space must be a singleton provided that each point in the space has a unique farthest point in the set. This classical result has received much attention; in fact, the Hilbert space version is a famous open problem. In this paper, we consider Klee sets from a new perspective. Rather than measuring distance induced by a norm, we focus on the case...
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Which point sets realize a given distance multiset? Interesting cases include the “turnpike problem” where the points lie on a line, the “beltway problem” where the points lie on a loop, and multidimensional versions. We are interested both in the algorithmic problem of determining such point sets for a given collection of distances and the combinatorial problem of finding bounds on the maximum...
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ژورنال
عنوان ژورنال: Involve, a Journal of Mathematics
سال: 2020
ISSN: 1944-4184,1944-4176
DOI: 10.2140/involve.2020.13.487