The Aharoni--Korman conjecture is false

Lawrence Hollom

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arXiv · 2411.16844

The Aharoni--Korman conjecture is false

Lawrence Hollom

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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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Lawrence Hollom. 2026-07-02. The Aharoni--Korman conjecture is false. https://arxiv.org/abs/2411.16844

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