Rachůnek, Jiří The ordinal variety of distributive ordered sets of width two. (English) Zbl 0773.06006 Acta Univ. Palacki. Olomuc., Fac. Rerum Nat. 100, Math. 30, 17-32 (1991). An ordered set \(P\) is said to be distributive if \(L(U(a,b),c)=LU(L(a,c),L(b,c))\), where \(L(X)\) and \(U(X)\) denote the sets of all lower and upper bounds of a subset \(X\) in \(P\) respectively. The author looks for ordinally irreducible distributive ordered sets of width two. Reviewer: J.Niederle (Brno) Cited in 2 Documents MSC: 06A07 Combinatorics of partially ordered sets Keywords:distributivity; ordinally irreducible ordered set PDF BibTeX XML Cite \textit{J. Rachůnek}, Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 30, 17--32 (1991; Zbl 0773.06006) OpenURL References: [1] Chajda I., Rachůnek J.: Forbidden configurations for distributive and modular ordered sets. Order 5 (1989), 407-423. · Zbl 0674.06003 [2] Duffus D., Rival I.: A structure theory for ordered sets. Discrete Math. 35 (1981), 53-118. · Zbl 0459.06002 [3] Larmerová J., Rachůnek J.: Translations of distributive and modular ordered sets. Acta Univ.Palack. Olomucensis, Fac. Rer. Nat. Math. 91 (1988), 13-23. · Zbl 0693.06003 [4] Rachůnek J.: Ordinal varieties of ordered sets. · Zbl 0736.06008 [5] Skornjakov L.A.: Elements of Lattice Theory. (Russian), Nauka, Moscow, 1970. · Zbl 0312.16020 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.