Partitions of the 8-Dimensional Vector Space Over GF(2)

• 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 Sigma(n)(i=1) a(i)(q(i)-1) = q(n)-1, and we call the n-tuple (a(n), a(n-1), ..., a(1)) the type of P. In this article we identify all 8-tuples (a(8), a(7), ..., a(2), 0) that are the types of partitions of V(8,2).

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NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

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Vector space partition

MATHEMATICS

MATEMATIK

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