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A finite set covering theorem III
Published online by Cambridge University Press: 17 April 2009
Abstract
Let n, s, t be integers with s > t > 2. If a family of n different subsets of a set S, with s elements, has the properties, (i) each member belongs to a set of (t+1) members which together have union S, (ii) no member belongs to a set of t members which together have union S, then we prove that n ≤ (t+1)s−t−1. The result is best possible.
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- Copyright © Australian Mathematical Society 1972
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