Titlebook: Lattice Theory: Special Topics and Applications; Volume 2 George Grätzer,Friedrich Wehrung Book 2016 Springer International Publishing Swit

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Convex Geometries,ion of convexity. Similarly, the theory of matroids is a combinatorial abstraction of independent sets; see the survey of B. Dietrich [125]. Since both abstractions can be formulated in the framework of a closure operator on a finite set, one can associate with a convex geometry or a matroid the clo

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Bases of Closure Systems,nical forms of representations of a closure system by implications. Most of the results are inspired by the structure of the closure lattice and its properties. In particular, we will be concerned with effective representations of closure systems whose closure lattices are join-semidistributive, low

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Finite Coxeter Groups and the Weak Order,nts to this chapter: First, to show how the geometry and lattice theory of hyperplane arrangements underlies the theory of finite Coxeter groups, and second, to point out the weak orders on finite Coxeter groups as an important class of lattice-theoretic examples. A broader class of examples is obta

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