Abstract
We define nonextendible colored posets and zigzags of a poset. These notions are related to the earlier notions of gaps, holes, obstructions and zigzags considered by Duffus, Nevermann, Rival, Tardos and Wille. We establish some properties of zigzags. By using these properties we give a proof of the well known conjecture that states that any finite bounded poset which admits Jńsson operations, also admits a near unanimity function. We also provide an infinite poset that shows that we cannot drop the finiteness in this conjecture.
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Zádori, L. Monotone Jónsson operations and near unanimity functions. Algebra Universalis 33, 216–236 (1995). https://doi.org/10.1007/BF01190934
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DOI: https://doi.org/10.1007/BF01190934