Lattices with few distances
نویسندگان
چکیده
منابع مشابه
Lattices with Few Distances*
The n-dimensional lattices that contain fewest distances are characterized for all n ≠ 2. ___________* This paper appeared in J. Number Theory, 39 (1991), 75-90. It is also DIMACS Technical Report 90-77,December 1990.
متن کاملTwo-dimensional lattices with few distances
We prove that of all two-dimensional lattices of covolume 1 the hexagonal lattice has asymptotically the fewest distances. An analogous result for dimensions 3 to 8 was proved in 1991 by Conway and Sloane. Moreover, we give a survey of some related literature, in particular progress on a conjecture from 1995 due to Schmutz Schaller.
متن کاملHypercube Embedding of Distances with Few Values Hypercube Embedding of Distances with Few Values
A distance d on a nite set V is hypercube embeddable if it can be isometrically embedded into the hypercube f0; 1g m for some m 1, i.e., if the elements i 2 V can be labeled by sets A i in such a way that d(i; j) = jA i 4A j j for all i; j 2 V. Testing whether a distance d is hypercube embeddable is an NP-complete problem, even if d is assumed to take its values in f2; 3; 4; 6g ((Chv80]). On th...
متن کاملTwo-dimensional lattices with few distances by Pieter MOREE and Robert OSBURN
We prove that of all two-dimensional lattices of covolume 1 the hexagonal lattice has asymptotically the fewest distances. An analogous result for dimensions 3 to 8 was proved in 1991 by Conway and Sloane. Moreover, we give a survey of some related literature, in particular progress on a conjecture from 1995 due to Schmutz Schaller.
متن کاملBounds on sets with few distances
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: • we improve the Ray-Chaudhuri–Wilson bound of the size of uniform intersecting families of subsets; • we refine the bound of Delsarte-Goethals-Seidel on the maximum size of spherical sets with few distances; • we prove a new bound on codes with few dista...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1991
ISSN: 0022-314X
DOI: 10.1016/0022-314x(91)90035-a