


























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.
From: Lawrence Hollom [view email]
[v1]
Mon, 25 Nov 2024 19:00:01 UTC (58 KB)
[v2]
Fri, 20 Dec 2024 15:25:14 UTC (59 KB)
[v3]
Wed, 15 Jan 2025 12:52:10 UTC (60 KB)
[v4]
Thu, 22 May 2025 16:43:52 UTC (61 KB)
[v5]
Thu, 2 Jul 2026 17:49:31 UTC (17 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理,仅供阅读参考。 原文来自 — 版权归原作者所有。