Antichains of fixed diameter
نویسنده
چکیده
The main result of the paper is to prove for every r ≥ 0 and n > n0(r) that every antichain on n vertices and consisting of more than ( n r ) sets contains two members whose symmetric difference is at least 2r + 2. The bound is best possible and all the extremal families are determined. For r ≥ 3 we show that n > 6(r + 1)2 is sufficient.
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