The minimum size of a finite subspace partition |
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Authors: | Esmeralda L. N?stase |
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Affiliation: | a Mathematics Department, Xavier University, 3800 Victory Parkway, Cincinnati, OH 45207, USA b Mathematics Department, Illinois State University, Normal, IL 61790, USA |
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Abstract: | A subspace partition of P=PG(n,q) is a collection of subspaces of P whose pairwise intersection is empty. Let σq(n,t) denote the minimum size (i.e., minimum number of subspaces) in a subspace partition of P in which the largest subspace has dimension t. In this paper, we determine the value of σq(n,t) for . Moreover, we use the value of σq(2t+2,t) to find the minimum size of a maximal partial t-spread in PG(3t+2,q). |
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Keywords: | 51E14 51E23 51E10 |
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