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The Aharoni--Korman conjecture is false
arXiv Math
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이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.Abstract
A poset $P$ is said to satisfy the finite antichain condition, or FAC, if it has no infinite antichain.
It was conjectured by Aharoni and Korman in 1992 that any FAC poset $P$ possesses a chain $C$ and a partition into antichains such that $C$ meets every antichain of the partition.
In this work we provide a counterexample to this conjecture, demonstrating that it is false.
We also discuss variations of the conjecture which may yet be true.
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