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Maximum number of constant weight vertices of the unit n–cube contained in a k–dimensional subspace
 COMBINATORICA
, 2003
"... We introduce and solve a natural} geometrical extremal problem. For the set E(n,w) = n n n n x ∈{0,1}:x has w ones of vertices of weight w in the unit cube of R we determine M(n,k,w)�max { U n k ∩E(n,w):U n k is a kdimensional subspace of R n}. We also present an extension to multi–sets and expla ..."
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Cited by 8 (2 self)
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We introduce and solve a natural} geometrical extremal problem. For the set E(n,w) = n n n n x ∈{0,1}:x has w ones of vertices of weight w in the unit cube of R we determine M(n,k,w)�max { U n k ∩E(n,w):U n k is a kdimensional subspace of R n}. We also present an extension to multi
Key words and phrases. Geometric probability, random subspace.
"... ABSTRACT. We determine the probability that a random kdimensional subspace ofRn contains a positive vector. For positive integers k and nwith k ≤ n, let p(n, k) denote the probability that a random kdimensional subspace of Rn contains a positive vector. The aim of this article is to prove (1) p(n, ..."
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ABSTRACT. We determine the probability that a random kdimensional subspace ofRn contains a positive vector. For positive integers k and nwith k ≤ n, let p(n, k) denote the probability that a random kdimensional subspace of Rn contains a positive vector. The aim of this article is to prove (1) p
COVERING BY COMPLEMENTS OF SUBSPACES, II
"... Abstract. Let V be an ndimensional vector space over an algebraically closed field K. Define γ(k, n, K) to be the least positive integer t for which there exists a family E1,E2,...,Et of kdimensional subspaces of V such that every (n−k)dimensional subspace F of V has at least one complement among ..."
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Abstract. Let V be an ndimensional vector space over an algebraically closed field K. Define γ(k, n, K) to be the least positive integer t for which there exists a family E1,E2,...,Et of kdimensional subspaces of V such that every (n−k)dimensional subspace F of V has at least one complement
ABSTRACT SamplingBased Dimension Reduction for Subspace Approximation
"... We give a randomized bicriteria algorithm for the problem of finding a kdimensional subspace that minimizes the Lperror for given points, i.e., pth root of the sum of pth powers of distances to given points, for any p ≥ 1. Our algorithm runs in time Õ ` mn · k 3 (k/ɛ) p+1 ´ and produces a subse ..."
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Cited by 14 (1 self)
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We give a randomized bicriteria algorithm for the problem of finding a kdimensional subspace that minimizes the Lperror for given points, i.e., pth root of the sum of pth powers of distances to given points, for any p ≥ 1. Our algorithm runs in time Õ ` mn · k 3 (k/ɛ) p+1 ´ and produces a
Sampling Based Dimension Reduction for Subspace Approximation
"... We give a randomized bicriteria algorithm for the problem of finding a kdimensional subspace that minimizes the Lperror for given points, i.e., pth root of the sum of pth powers of distances to given points, for any p ≥ 1. Our algorithm runs in time Õ ( mn · k 3 (k/ɛ) p+1) and produces a subset ..."
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We give a randomized bicriteria algorithm for the problem of finding a kdimensional subspace that minimizes the Lperror for given points, i.e., pth root of the sum of pth powers of distances to given points, for any p ≥ 1. Our algorithm runs in time Õ ( mn · k 3 (k/ɛ) p+1) and produces a
TwoWeight Codes with prescribed Symmetries
"... Linear [n,k,q] codes are k–dimensional subspaces C of the n–dimensional vectorspace GF(q) n. They are described by a generator matrix, i.e. a matrix whose rows are a basis of C. ..."
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Linear [n,k,q] codes are k–dimensional subspaces C of the n–dimensional vectorspace GF(q) n. They are described by a generator matrix, i.e. a matrix whose rows are a basis of C.
kHYPERREFLEXIVE SUBSPACES
, 2006
"... Changing rankone operators in a suitable definition of hyperreflexivity to rank k operators we give a definition of khyperreflexivity. We give an example of 2hyperreflexive subspace S such that S(2) is not hyperreflexive. There are also given properties and examples of khyperreflexivity. It i ..."
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Cited by 6 (2 self)
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hyperreflexivity. It is shown that the space of all Toeplitz operators is 2hyperreflexive and each kdimensional subspace is khyperreflexive.
ON PROJECTIVE EQUIVALENCE OF UNIVARIATE POLYNOMIAL SUBSPACES.
, 902
"... Abstract. We pose and solve the equivalence problem for subspaces of Pn, the (n + 1) dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is SL2 acting by projective transformations on the Grassmannian variety GkPn of kdimensional subspaces. We establish the equiv ..."
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Cited by 3 (1 self)
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Abstract. We pose and solve the equivalence problem for subspaces of Pn, the (n + 1) dimensional vector space of univariate polynomials of degree ≤ n. The group of interest is SL2 acting by projective transformations on the Grassmannian variety GkPn of kdimensional subspaces. We establish
NORMALIZED MATCHING PROPERTY OF A CLASS OF SUBSPACE LATTICES
"... Abstract. Let Vn(q) be the ndimensional vector space over the finite field with q elements and K a selected kdimensional subspace of Vn(q). Let C[n, k, t] denote the set of all subspaces S’s such that dim(S ∩ K) ≥ t. We show that C[n, k, t] has the normalized matching property, which yields that ..."
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Cited by 2 (1 self)
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Abstract. Let Vn(q) be the ndimensional vector space over the finite field with q elements and K a selected kdimensional subspace of Vn(q). Let C[n, k, t] denote the set of all subspaces S’s such that dim(S ∩ K) ≥ t. We show that C[n, k, t] has the normalized matching property, which yields
Colouring Subspaces
, 2005
"... This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the qKneser graph are the kdimensional subspaces of a vector sp ..."
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This thesis was originally motivated by considering vector space analogues of problems in extremal set theory, but our main results concern colouring a graph that is intimately related to these vector space analogues. The vertices of the qKneser graph are the kdimensional subspaces of a vector
Results 1  10
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44,254