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The rank of a distributive lattice
Discrete Mathematics, 1979 AbstractThe rank of a partial ordering P is the maximum size of an irredundant family of linear extensions of P whose intersection is P. A simple relationship is established between the rank of a finite distributive lattice and its subset of join irreducible elements.
I. Rabinovitch, I. Rival
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Decomposition theorem on matchable distributive lattices
, 2010 A distributive lattice structure ${\mathbf M}(G)$ has been established on the set of perfect matchings of a plane bipartite graph $G$. We call a lattice {\em matchable distributive lattice} (simply MDL) if it is isomorphic to such a distributive lattice.
Birkhoff +33 more
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μ-Fuzzy Filters in Distributive Lattices
Advances in Fuzzy Systems, 2020 In this paper, we introduce the concept of μ-fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ-fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators.
Wondwosen Zemene Norahun
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Sahlqvist via Translation [PDF]
Logical Methods in Computer Science, 2019 In recent years, unified correspondence has been developed as a generalized Sahlqvist theory which applies uniformly to all signatures of normal and regular (distributive) lattice expansions.
Willem Conradie +2 more
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Congruences on a Distributive Lattice [PDF]
Proceedings of the Edinburgh Mathematical Society, 1954 Among the many papers on the subject of lattices I have not seen any simple discussion of the congruences on a distributive lattice. It is the purpose of this note to give such a discussion for lattices with a certain finiteness. Any distributive lattice is isomorphic with a ring of sets (G. Birkhoff, Lattice Theory, revised edition, 1948, p.
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“Complete-simple” distributive lattices [PDF]
Proceedings of the American Mathematical Society, 1993 It is well known that the only simple distributive lattice is the two-element chain. We can generalize the concept of a simple lattice to complete lattices as follows: a complete lattice is complete-simple if it has only the two trivial complete congruences.
Grätzer, G., Schmidt, E. T.
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f-Fixed Points of Isotone f-Derivations on a Lattice
Discussiones Mathematicae - General Algebra and Applications, 2019 In a recent paper, Çeven and Öztürk have generalized the notion of derivation on a lattice to f-derivation, where f is a given function of that lattice into itself.
Zedam Lemnaouar +2 more
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The annihilator graph of a 0-distributive lattice [PDF]
Transactions on Combinatorics, 2018 In this article, for a lattice $\mathcal L$, we define and investigate the annihilator graph $\mathfrak {ag} (\mathcal L)$ of $\mathcal L$ which contains the zero-divisor graph of $\mathcal L$ as a subgraph. Also, for a 0-distributive lattice
Saeid Bagheri, Mahtab Koohi Kerahroodi
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A class of multipartner matching markets with a strong lattice structure [PDF]
, 2002 For a two-sided multipartner matching model where agents are given by path-independent choice functions and no quota restrictions, Blair [7] had shown that stable matchings always exist and form a lattice.
Alkan, Ahmet
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On the Homology of Distributive Lattices
European Journal of Combinatorics, 1998 For a finite poset \(P\) the set of order-ideals \(J(P)=L\) ordered by containment is a distributive lattice with rank \(| P|\) and rank function \(\rho(I) =| I|\). If \(S\subseteq [n-1]= \{1,\dots, n-1\}\), then \(J(P)_S= \{I\in J(P) \mid| I|\in S\cup \{0,n\}\}\). Given a finite poset \(Q=J(P)_S\) with \(\widehat 0\) and \(\widehat 1\), let \(C_r(Q)\),
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