On the type(s) of minimum size subspace partitions

• Let V = V(kt + r, q) be a vector space of dimension kt + r over the finite field with q elements. Let sigma(q)(kt + r, t) denote the minimum size of a subspace partition P of V in which t is the largest dimension of a subspace. We denote by n(di) the number of subspaces of dimension d(i) that occur in P and we say [d(1)(nd1),..., d(m)(ndm)] is the type of P. In this paper, we show that a partition of minimum size has a unique partition type if t + r is an even integer. We also consider the case when t + r is an odd integer, but only give partial results since this case is indeed more intricate.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Vector space partitions

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