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A resolution of the Aharoni--Korman conjecture

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  • UserLawrence Hollom (Cambridge)
  • ClockThursday 16 October 2025, 14:30-15:30
  • HouseMR12.

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The Aharoni—Korman conjecture, also known as the fishbone conjecture, states that any poset contains a chain C and a partition into antichains such that C meets every antichain in the partition. Our results are twofold. Firstly, we construct a poset for which the conjecture is false. Secondly, we demonstrate that this counterexample is, in some sense, minimal, giving a strong positive result which shows that the conjecture is true if one makes an additional assumption about the structure of the poset.

This talk is part of the Combinatorics Seminar series.

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