Covering by complements of subspaces, II
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- by W. Edwin Clark and Boris Shekhtman PDF
- Proc. Amer. Math. Soc. 125 (1997), 251-254 Request permission
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
- W. Edwin Clark and Boris Shekhtman, Covering by complements of subspaces, Linear and Multilinear Algebra 40 (1995), 1–13. CMP 96:08
- —, Domination numbers of q-analogues of Kneser graphs, Bulletin of the Institute of Combinatorics and its Applications (to appear).
- Joe Harris, Algebraic geometry, Graduate Texts in Mathematics, vol. 133, Springer-Verlag, New York, 1992. A first course. MR 1182558, DOI 10.1007/978-1-4757-2189-8
Additional Information
- W. Edwin Clark
- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- MR Author ID: 49750
- Email: eclark@math.usf.edu
- Boris Shekhtman
- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- MR Author ID: 195882
- Email: boris@math.usf.edu
- Received by editor(s): November 22, 1994
- Received by editor(s) in revised form: July 6, 1995
- Communicated by: Jeffry N. Kahn
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 251-254
- MSC (1991): Primary 51A99; Secondary 14N10, 15A75, 15A99
- DOI: https://doi.org/10.1090/S0002-9939-97-03535-1
- MathSciNet review: 1346967