Ordered Sets: An Introduction with Connections from Combinatorics to Topology

Description

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. Front Matter....Pages i-xvi Basics....Pages 1-21 Chains, Antichains, and Fences....Pages 23-51 Upper and Lower Bounds....Pages 53-76 Retractions....Pages 77-111 Constraint Satisfaction Problems....Pages 113-153 Graphs and Homomorphisms....Pages 155-171 Lexicographic Sums....Pages 173-197 Lattices....Pages 199-226 Truncated Lattices....Pages 227-253 Dimension....Pages 255-277 Interval Orders....Pages 279-295 Sets P Q  = Hom(Q, P) and Products ....Pages 297-332 Enumeration of Ordered Sets....Pages 333-356 Back Matter....Pages 357-420