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Covering by complements of subspaces, II

Authors:	W Edwin Clark Boris Shekhtman

Institution:	Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700 ; Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700

Abstract:	Let be an -dimensional vector space over an algebraically closed field . Define $\gamma (k,n,K)$ to be the least positive integer for which there exists a family $E_{1}, E_{2}, \dots , E_{t}$ of -dimensional subspaces of such that every -dimensional subspace of has at least one complement among the $E_{i}$ 's. Using algebraic geometry we prove that $\gamma (k,n,K) = k(n-k) +1$ .

Keywords:	Vector space subspace complement projective variety Grassmannian

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