Partitions of V(n,q) into 2‐ and s‐Dimensional Subspaces |
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Authors: | G Seelinger P Sissokho L Spence C Vanden Eynden |
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Abstract: | Let denote a vector space of dimension n over the field with q elements. A set of subspaces of V is a (vector space) partition of V if every nonzero element of V is contained in exactly one subspace in . Suppose that is a partition of V with subspaces of dimension for . Then we call the type of the partition . Which possible types correspond to actual partitions is in general an open question. We prove that for any odd integer and for any integer , the existence of partitions of across a suitable range of types guarantees the existence of partitions of of essentially all the types for any integer . We then apply this result to construct new classes of partitions of V. © 2012 Wiley Periodicals, Inc. J. Combin. Designs 20: 467‐482, 2012 |
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Keywords: | vector space partition subspace partition partition type |
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