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On congruence lattices of lattices
Algebra Universalis, 1985This paper concerns the old problem, whether every distributive algebraic lattice is isomorphic to the congruence lattice of a lattice. The author discovers a new approach to reduce the representation problem to investigations of congruence lattices of finite lattices. His approach is the following. Let D be the category of finite distributive lattices
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Graphs and Combinatorics, 2002
A pair \((x,y)\) of elements in a lattice is said to be mismatching if \(x\) is join-irreducible, \(y\) is meet-irreducible and \(x\nleqslant y\). The excess of a lattice \(L\) is the number \(\text{ex}(L) =|L|-\min \{|V_x|+ |I_y|\): \((x,y)\) is a mismatching pair\}, where \(V_x\) and \(I_y\) are the filter generated by \(x\) and the ideal generated ...
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A pair \((x,y)\) of elements in a lattice is said to be mismatching if \(x\) is join-irreducible, \(y\) is meet-irreducible and \(x\nleqslant y\). The excess of a lattice \(L\) is the number \(\text{ex}(L) =|L|-\min \{|V_x|+ |I_y|\): \((x,y)\) is a mismatching pair\}, where \(V_x\) and \(I_y\) are the filter generated by \(x\) and the ideal generated ...
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Review on lattice structures for energy absorption properties
Composite Structures, 2023Guilin Wen, Hanfeng Yin
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Lattices and Lattice Complexes
1991A lattice is an array of points each of which has identical environment in identical orientation. The points of a lattice are related to each other by a translation: by moving the entire lattice parallel to itself through an appropriate distance it can be brought into coincidence with itself (cf. Fig. 15-1).
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Charge-carrier-mediated lattice softening contributes to high zT in thermoelectric semiconductors
Joule, 2021Tyler Slade +2 more
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