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(s, k, λ)-Partitions of a vector space

✍ Scribed by Antonino Giorgio Spera

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
309 KB
Volume
89
Category
Article
ISSN
0012-365X

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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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## Abstract Let __V__~n~(q) denote a vector space of dimension __n__ over the field with __q__ elements. A set ${\cal P}$ of subspaces of __V__~n~(q) is a __partition__ of __V__~n~(q) if every nonzero element of __V__~n~(q) is contained in exactly one element of ${\cal P}$. Suppose there exists a p