The “k = 1” Case of a Problem of Greene and Kleitman from 1976: Join-Irreducible Elements in the Lattice of Sperner 1-Families
Let k ≥ 1. A Sperner k-family is a maximum-sized subset of a finite poset that contains no chain with k + 1 elements. In 1976 Greene and Kleitman defined a lattice-ordering on the set Sk(P) of Sperner k-families of a fifinite poset P and posed the problem: “Characterize and interpret the join- and meet-irreducible elements of Sk(P),” adding, “This has apparently not been done even for the case k = 1.”In this article, the case k = 1 is done.
2018 ◽
Vol 62
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pp. 395-442
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2000 ◽
Vol 68
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pp. 85-103
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1973 ◽
Vol 45
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pp. 555-560
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1971 ◽
Vol 23
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pp. 866-874
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