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Rank Bounded Hibi Subrings for Planar Distributive Lattices [PDF]
, 2019 Let $L$ be a distributive lattice and $R[L]$ the associated Hibi ring. We show that if $L$ is planar, then any bounded Hibi subring of $R[L]$ has a quadratic Gr\"obner basis.
Rida Irfan, Nadia Shoukat
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Distributive lattices have the intersection property [PDF]
Mathematica Bohemica, 2021 Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices.
Henri Mühle
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Total graph of a $0$-distributive lattice [PDF]
Categories and General Algebraic Structures with Applications, 2018 Let £ be a $0$-distributive lattice with the least element $0$, the greatest element $1$, and ${rm Z}(£)$ its set of zero-divisors. In this paper, we introduce the total graph of £, denoted by ${rm T}(G (£))$.
Shahabaddin Ebrahimi Atani +3 more
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CD-independent subsets in meet-distributive lattices [PDF]
, 2013 A subset $X$ of a finite lattice $L$ is CD-independent if the meet of any two incomparable elements of $X$ equals 0. In 2009, Cz\'edli, Hartmann and Schmidt proved that any two maximal CD-independent subsets of a finite distributive lattice have the same
Gábor Czédli
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Homology of Distributive Lattices [PDF]
Journal of Homotopy and Related Structures, 2011 We outline the theory of sets with distributive operations: multishelves and multispindles, with examples provided by semi-lattices, lattices and skew lattices.
A. Frabetti +24 more
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Distributive mereotopology: extended distributive contact lattices [PDF]
Annals of Mathematics and Artificial Intelligence, 2016 Contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with a relation called contact. The elements of the Boolean algebra are considered as formal representations of physical bodies. The contact relation is used also to define some other important mereotopological relations like non ...
T. Ivanova, Dimiter Vakarelov
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Bounded distributive lattice expansions
MATHEMATICA SCANDINAVICA, 2004 A new notion of a canonical extension $\mathbf{A}^{\sigma }$ is introduced that applies to arbitrary bounded distributive lattice expansions (DLEs) $\mathbf{A} $. The new definition agrees with the earlier ones whenever they apply. In particular, for a bounded distributive lattice $\mathbf{A}, \mathbf{A}^{\sigma }$ has the same meaning as before.
M. Gehrke, B. Jónsson
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Distributive lattices determined by weighted double skeletons
, 2013 Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive lattice and its second skeleton, S(S(D)), is the trivial lattice, then D is ...
Gábor Czédli +2 more
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Some Properties of Generalized Intuitionistic Fuzzy Nilpotent Matrices over Distributive Lattice [PDF]
, 2012 Amal Kumar Adak +2 more
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Meet-distributive lattices have the intersection property [PDF]
Mathematica Bohemica, 2023 This paper is an erratum of H. Mühle: Distributive lattices have the intersection property, Math. Bohem. (2021). Meet-distributive lattices form an intriguing class of lattices, because they are precisely the lattices obtainable from a closure operator ...
Henri Mühle
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