Some necessary conditions for vector space partitions

• Some new necessary conditions for the existence of vector space partitions are derived. They are applied to the problem of finding the maximum number of spaces of dimension t in a vector space partition of V(2t, q) that contains m(d) spaces of dimension d, where t/2 < d < t, and also spaces of other dimensions. It is also discussed how this problem is related to maximal partial t-spreads in V (2t, q). We also give a lower bound for the number of spaces in a vector space partition and verify that this bound is tight.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Vector space partition

Partial spread

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