Combinatorics and Partially Ordered Sets

Dimension Theory
Erscheinungsjahr 1992
ISBN: 978-0-8018-6977-8
Verlag: Johns Hopkins University Press

Buch, Englisch, Band 6, 328 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 528 g

Reihe: Johns Hopkins Studies in the Mathematical Sciences

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.

Autoren/Hrsg.

Trotter, William T.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Introduction to Dimension
Chapter 1. Crowns, Splits, Stacks, Sums and Products
Chapter 2. Characterization Problems for Posets, Lattices, Graphs, and Families of Sets
Chapter 3. Hypergraph Coloring, Computational Complexity and Irreducible Posets
Chapter 4. Planar Maps, and Convex Polytopes
Chapter 5. Probabilistic Methods in Dimension Theory
Chapter 6. Interval and Geometric Containment Orders
Chapter 7. Greedy Dimension, Back-Tracking and Depth First Search
Chapter 8. Products of Chains of Bounded Length
Chapter 9. Large Minimal Realizers

Über Autor(innen)

Trotter, William T.
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.