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 mathematicsincluding 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
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 mathematicsincluding 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
The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of...
The discrete mathematics and theoretical computer science communities have recently witnessed explosive growth in the area of algorithmic combinatorics on words. The next generation of research on...
Recently the theory of partially ordered groups has been used by analysts, algebraists, topologists and model theorists. This book presents the most important results and topics in the theory with...
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