Lattice Theory: Special Topics and Applications [electronic resource] : Volume 2 /
Grätzer, George.editor.
Wehrung, Friedrich.editor.
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.
Includes bibliographical references and indexes.
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.
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.
Algebra.
Ordered algebraic structures.
Convex geometry .
Discrete geometry.
Polytopes.
Order, Lattices, Ordered Algebraic Structures.
Convex and Discrete Geometry.
Polytopes.