Affine and combinatorial binary m-spaces |
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Authors: | TC Brown |
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Institution: | Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada |
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Abstract: | Let V(n) denote the n-dimensional vector space over the 2-element field. Let a(m, r) (respectively, c(m, r)) denote the smallest positive integer such that if n ? a(m, r) (respectively, n ? c(m, r)), and V(n) is arbitrarily partitioned into r classes Ci, 1 ? i ? r, then some class Ci must contain an m-dimensional affine (respectively, combinatorial) subspace of V(n). Upper bounds for the functions a(m, r) and c(m, r) are investigated, as are upper bounds for the corresponding “density functions” and . |
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