Abstract
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 ( 2 t , 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 ( 2 t , q ) . We also give a lower bound for the number of spaces in a vector space partition and verify that this bound is tight.
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