Abstract
A vector space partition of Fqv is a collection of subspaces such that every non-zero vector is contained in a unique element. We improve a lower bound of Heden, in a subcase, on the number of elements of the smallest occurring dimension in a vector space partition. To this end, we introduce the notion of qr-divisible sets of k-subspaces in Fqv. By geometric arguments we obtain non-existence results for these objects, which then imply the improved result of Heden.
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