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An Extremal Problem for Families of Pairs of Subspaces

โœ Scribed by Meir Katchalski; Roy Meshulam

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
108 KB
Volume
15
Category
Article
ISSN
0195-6698

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โœฆ Synopsis

We consider the following vector space analogue of a problem in extremal sel theory. Let (g(k, l)) denote the maximal (t) for which there exist (t) pairs of linear subspaces (\left(U_{1}, V_{1}\right) \ldots), (\left(U_{i}, V_{i}\right)) of a real vector space (H), such that (\operatorname{dim} U_{i}=k, \operatorname{dim} V_{i}=l, U_{i} \cap V_{i}=0) and for any (1 \leqslant i \neq j \leqslant t), either (U_{i} \cap V_{j} \neq 0) or (U_{j} \cap V_{i} \neq 0).

It is shown that

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