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On the length of the tail of a vector space partition

✍ Scribed by Olof Heden

Book ID: 108114162
Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 602 KB
Volume: 309
Category: Article
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.05.026

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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) =