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Partitions of V(n, q) into 2- and s-Dimensional Subspaces

✍ Scribed by G. Seelinger; P. Sissokho; L. Spence; C. Vanden Eynden

Book ID
112120472
Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
528 KB
Volume
20
Category
Article
ISSN
1063-8539

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πŸ“œ SIMILAR VOLUMES

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✍ S. I. El-Zanati; G. F. Seelinger; P. A. Sissokho; L. E. Spence; C. Vanden Eynden πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 143 KB

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Let V = V(n,q) denote the vector space of dimension n over GF(q). A set of subspaces of V is called a partition of V if every nonzero vector in V is contained in exactly one subspace of V. Given a partition P of V with exactly a i subspaces of dimension i for 1 ≀ i ≀ n, we have n i=1 a i (q i -1) =

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A longstanding conjecture of Reay asserts that every set X of (m-1)(d +1)+k+1 points in general position in R d has a partition X 1 , X 2 , . . . , X m such that m i=1 conv X i is at least k-dimensional. Using the tools developed in [13] and oriented matroid theory, we prove this conjecture for d =