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- W3213974985 abstract "Let X and Z be finite disjoint sets and let y be a point not contained in XZ. Marcel Erné showed in 1981, that the number of posets on XZ containing Z as an antichain equals the number of posets R on XZy in which the points of Z{y} are exactly the maximal points of R. We prove the following generalization: For every poset Q with carrier Z, the number of posets on XZ containing Q as an induced sub-poset equals the number of posets R on X ∪ Z ∪{y} which contain Q + y as an induced sub-poset and in which the maximal points of Q + y are exactly the maximal points of R. Here, Q + y denotes the direct sum of Q and the singleton-poset on y." @default.
- W3213974985 created "2021-11-22" @default.
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- W3213974985 date "2021-11-11" @default.
- W3213974985 modified "2023-09-24" @default.
- W3213974985 title "A Generalization of a Theorem of Erné about the Number of Posets with a Fixed Antichain" @default.
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