Title: Combinatorics and Partially Ordered Sets: Dimension Theory (Johns Hopkins Studies in the Mathematical Sciences)
Publisher: The Johns Hopkins University Press
Publication Date: 1992
Language: English
ISBN 10: 0801844258
ISBN 13: 9780801844256
Binding: Hardcover
Condition: Very Good
Dust Jacket Condition: No Jacket

About this title

Synopsis

Primarily intended for research mathematicians and computer scientists, Combinatorics and Partially Ordered Sets: Dimension Theory also serves as a useful text for advanced students in either field. William Trotter concentrates on combinatorial topics for finite partially ordered sets, and with dimension theory serving as a unifying theme, research on partially ordered sets or posets is linked to more traditional topics in combinatorial mathematics -- including graph theory, Ramsey theory, probabilistic methods, hypergraphs, algorithms, and computational geometry. The book's most important contribution is to collect, organize, and explain the many theorems on partially ordered sets in a way that makes them available to the widest possible audience.

Chapters: Introduction to Dimension � Crowns, Splits, Stacks, Sums and Products � Characterization Problems for Posets, Lattices, Graphs, and Families of Sets � Hypergraph Coloring, Computational Complexity, and Irreducible Posets � Planar Posets and Trees � Planar Graphs, Planar Maps and Convex Polytopes � Probabilistic Methods in Dimension Theory � Interval and Geometric Containment Orders � Greedy Dimension, Back-Tracking, and Depth First Search � Products of Chains of Bounded Length � Large Minimal Realizers

About the Author

William T. Trotter is Regents' Professor of Mathematics at Arizona State University and director of Combinatorics and Operations Research for Bell Communications Research in Morristown, New Jersey.

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