Greene-Kleitman's theorem for infinite posets |
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Authors: | Ron Aharoni Vladimir Korman |
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Institution: | (1) Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel |
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Abstract: | It is proved that if (P) is a poset with no infinite chain and k is a positive integer, then there exist a partition of P into disjoint chains C
i and disjoint antichains A
1, A
2, ..., A
k, such that each chain C
i meets min (k, |C
i|) antichains A
j. We make a dual conjecture, for which the case k=1 is: if (P) is a poset with no infinite antichain, then there exist a partition of P into antichains A
i and a chain C meeting all A
i. This conjecture is proved when the maximal size of an antichain in P is 2. |
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Keywords: | 06A06 |
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