Ordered Sets

An Introduction with Connections from Combinatorics to Topology
2. Auflage 2016
ISBN: 978-3-319-29786-6
Verlag: Springer International Publishing

Buch, Englisch, 420 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 8535 g

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets.  The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Zielgruppe

Graduate

Autoren/Hrsg.

Schröder, Bernd

Fachgebiete

• Mathematik | Informatik Mathematik Topologie
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik

Inhaltsverzeichnis

Preface.- Basics.- Chains, Antichains, and Fences.- Upper and Lower Bounds.- Retractions.- Constraint Satisfaction Problems.- Graphs and Homomorphisms.- Lexicographic Sums.- Lattices.- Truncated Lattices.- Dimension.- Interval Orders.- Sets P^Q = Hom (Q, P) and Products.- Enumeration of Ordered Sets.- Appendix A: Some Algebraic Topology.- Appendix B: Some Discrete Morse Theory.- References.- Index.

Über Autor(innen)

Bernd Schröder serves as Chair of the Department of Mathematics at The University of Southern Mississippi. In addition to teaching and service, he has published over 40 papers on subjects including ordered sets, graph theory, analysis, computer science, and engineering education.