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Basic Posets

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An introduction to the theory of partially-ordered sets, or "posets". The text is presented in rather an informal manner, with examples and computations, which rely on the Hasse diagram to build graphical intuition for the structure of infinite posets. The proofs of a small number of theorems is included in the appendix. Important examples, especially the Letter N poset, which plays a role akin to that of the Petersen graph in providing a candidate counterexample to many propositions, are used repeatedly throughout the text.

Author(s): Joseph Neggers, Hee Sik Kim
Edition: 1st
Publisher: World Scientific Pub Co Inc
Year: 1999

Language: English
Commentary: OCR, Front and Back Covers, Bookmarks, Pagination
Pages: 178

Preface
Chapter 1 Definitions and Examples
Chapter 2 How to Represent a Poset
2.1 Hasse Diagram
2.2 Labeling with a Hasse Diagram
2.3 The Adjacency Matrix of a Hasse Diagram
2.4 Interval Order and Semiorder
2.5 Angle Order and Circle Order
2.6 Other Representations
2.7 Order Geometry
Chapter 3 Poset Morphisms
Chapter 4 Construction of New Posets from Old Posets
4.1 Sum and Ordinal Sum
4.2 Product Order and Lexicographic Order
4.3 Exponential Posets
Chapter 5 Connectedness
Chapter 6 Linear Extensions
6.1 Linear Extensions
6.2 Representation Polynomials and Linear Extensions
6.3 Dimension
6.4 Applications of Linear Extensions
Appendix
References
Notations and Symbols
Index