The Aharoni--Korman conjecture is false

2024/11/25 by Lawrence Hollom, Hollom, Lawrence · 1 voice · 1 citation
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paper · pdf · doi:10.48550/arxiv.2411.16844

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.

Cited by

• Counterexamples to conjectures on strong maximality and minimality

Discussions

• A few days ago Lawrence Hollom posted a preprint that solves a problem about posets, informally known as the fishbone conjecture, which I am told was extremely central in the area. 🧵 arxiv.org/abs [bsky, 108 points, 1 comments]

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