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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Covering by complements of subspaces, II


Authors: W. Edwin Clark and Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 125 (1997), 251-254
MSC (1991): Primary 51A99; Secondary 14N10, 15A75, 15A99
MathSciNet review: 1346967
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Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)

  • 1. W. Edwin Clark and Boris Shekhtman, Covering by complements of subspaces, Linear and Multilinear Algebra 40 (1995), 1-13. CMP 96:08
  • 2. -, Domination numbers of q-analogues of Kneser graphs, Bulletin of the Institute of Combinatorics and its Applications (to appear).
  • 3. Joe Harris, Algebraic geometry, Graduate Texts in Mathematics, vol. 133, Springer-Verlag, New York, 1992. A first course. MR 1182558 (93j:14001)

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Additional Information

W. Edwin Clark
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: eclark@math.usf.edu

Boris Shekhtman
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: boris@math.usf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03535-1
PII: S 0002-9939(97)03535-1
Keywords: Vector space, subspace, complement, projective variety, Grassmannian
Received by editor(s): November 22, 1994
Received by editor(s) in revised form: July 6, 1995
Communicated by: Jeffry N. Kahn
Article copyright: © Copyright 1997 American Mathematical Society