Lattice Theory: Special Topics and Applications : Volume 2 / edited by George Grätzer, Friedrich Wehrung.

Format:

Book

Contributor:

Grätzer, George., Editor.

Wehrung, Friedrich., Editor.

Language:

English

Subjects (All):

Algebra.

Ordered algebraic structures.

Convex geometry.

Discrete geometry.

Polytopes.

Order, Lattices, Ordered Algebraic Structures.

Convex and Discrete Geometry.

Local Subjects:

Order, Lattices, Ordered Algebraic Structures.

Convex and Discrete Geometry.

Polytopes.

Physical Description:

1 online resource (XV, 616 p. 136 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Summary:

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.

Contents:

Varieties of Lattices

Free and Finitely Presented Lattices

Classes of Semidistributive Lattices

Lattices of Algebraic Subsets and Implicational Classes

Convex Geometries

Bases of Closure Systems

Permutohedra and Associahedra

Generalizations of the Permutohedron

Lattice Theory of the Poset of Regions

Finite Coxeter Groups and the Weak Order.

Notes:

Includes bibliographical references and indexes.