Abstract
We show that in an ordered setP of width 3 there always exists a fibre (i.e., a subset intersecting each maximal nontrivial antichain) of size at most 11/18|P|. This improves previously known results.
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Communicated by I. Rival
Research supported by Polish KBN Grant 2 2037 92 03.
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Lonc, Z. Fibres of width 3 ordered sets. Order 11, 149–158 (1994). https://doi.org/10.1007/BF01108599
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DOI: https://doi.org/10.1007/BF01108599