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• W2002564287 abstract "A theorem of Erdös, Ko and Rado states that if S is an n-element set and F is a family of k-element subsets of S, k⩽ 12n, such that no two members of F are disjoint, then …F… ⩽ (n - 1k - 1). In this paper we investigate the analogous problem for finite vector spaces. Let F be a family of k-dimensional subspaces of an n-dimensional vector space over a field of q elements such that members of F intersect pairwise non-trivially. Employing a method of Katona, we show that for n ⩾ 2k, …F… ⩽ (k/n) [nk]q. By a more detailed analysis, we obtain that for n ⩾ 2k + 1, …F… ⩽ [n - 1k - 1]q, which is a best possible bound. The argument employed is generalized to the problem of finding a bound on the size of F when its members have pairwise intersection dimension no smaller than r. Again best possible results are obtained for n ⩾ 2k + 2 and n ⩾ 2k + 1, q ⩾ 3. Application of these methods to the analogous subset problem leads to improvement on the Erdös-Ko-Rado bounds." @default.
• W2002564287 created "2016-06-24" @default.
• W2002564287 creator A5002078913 @default.
• W2002564287 date "1975-01-01" @default.
• W2002564287 modified "2023-09-30" @default.
• W2002564287 title "Intersection theorems for systems of finite vector spaces" @default.
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• W2002564287 doi "https://doi.org/10.1016/0012-365x(75)90091-6" @default.
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