منابع مشابه
Covering of subspaces by subspaces
Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...
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We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body C, symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of n-wise linearly independent lattice points in the n-dimensional ball rB of radius r around 0 is O(rn/(n−1)). This bound ...
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For any space X, denote by dis(X) the smallest (infinite) cardinal κ such that κ many discrete subspaces are needed to cover X. It is easy to see that if X is any crowded (i.e. dense-in-itself) compactum then dis(X) m, where m denotes the additivity of the meager ideal on the reals. It is a natural, and apparently quite difficult, question whether in this inequality m could be replaced by c. He...
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Let (U ′; C′) be a subspace of a covering approximation space (U ; C) and X ⊂ U ′. In this paper, we show that C′(X) = C(X)⋂ U ′ and B′(X) ⊂ B(X) ⋂ U ′. Also, C(X) = C′(X)⋂ C(U ′) iff (U ; C) has Property Multiplication. Furthermore, some connections between outer (resp. inner) definable subsets in (U ; C) and outer (resp. inner) definable subsets in (U ′; C′) are established. These results ans...
متن کاملApproximating weak Chebyshev subspaces by Chebyshev subspaces
We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties. r 2003 Elsevier Science (USA). All rights reserved.
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2012
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-012-9766-3