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Uniform Intersecting Families with Covering Number Restrictions
Published online by Cambridge University Press: 01 March 1998
Abstract
It is known that any k-uniform family with covering number t has at most ktt-covers. In this paper, we deal with intersecting families and give better upper bounds for the number of t-covers. Let pt(k) be the maximum number of t-covers in any k-uniform intersecting families with covering number t. We prove that, for a fixed t,
formula here
In the cases of t=4 and 5, we also prove that the coefficient of kt−1 in pt(k) is exactly (t2).
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- Research Article
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- 1998 Cambridge University Press
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