New Maximal Two-Distance Sets
نویسندگان
چکیده
منابع مشابه
New Maximal Two-Distance Sets
A two-distance set in E is a point set X in the d-dimensional Euclidean space such that the distances between distinct points in X assume only two different nonzero values. Based on results from classical distance geometry, we develop an algorithm to classify, for a given d, all maximal (largest possible) two-distance sets in E. Using this algorithm we have completed the full classification for...
متن کاملNew distance and similarity measures for hesitant fuzzy soft sets
The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and similarity measures are considered as the important tools in different areas such as ...
متن کاملSpherical two-distance sets
A set S of unit vectors in n−dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b so that the inner products of distinct vectors of S are either a or b. The largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n = 2, 6, 22. The set of midpoints of the edges of a regular simplex g...
متن کاملNew Bounds for Equiangular Lines and Spherical Two-Distance Sets
The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...
متن کاملSome results on maximal open sets
In this paper, the notion of maximal m-open set is introduced and itsproperties are investigated. Some results about existence of maximal m-open setsare given. Moreover, the relations between maximal m-open sets in an m-spaceand maximal open sets in the corresponding generated topology are considered.Our results are supported by examples and counterexamples.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1997
ISSN: 0097-3165
DOI: 10.1006/jcta.1997.2749