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A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
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Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician.His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right".
George A. Grätzer (Hungarian: Grätzer György; born 2 August 1936, in Budapest) is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is known for his books on LaTeX [1] and his proof with E. Tamás Schmidt of the Grätzer–Schmidt theorem. [2] [3]
[2]: 126 A function satisfies the one-dimensional wave equation if and only if it is a valuation for the lattice of spacetime coordinates with the natural partial order. A similar result should apply to any partial differential equation solvable by the method of characteristics, but key features of the theory are lacking. [2]: 150–151
A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented. [4] 17. A boolean algebra is relatively complemented. (1,15,16) 18. A relatively complemented lattice is a lattice. (def) 19. A heyting algebra is distributive. [5] 20. A totally ordered set is a ...
A Hasse diagram of Young's lattice. In mathematics, Young's lattice is a lattice that is formed by all integer partitions.It is named after Alfred Young, who, in a series of papers On quantitative substitutional analysis, developed the representation theory of the symmetric group.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.