76,40 €*
Versandkostenfrei per Post / DHL
Lieferzeit 1-2 Wochen
A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's, and Hashimoto's Theorems to more recent results such as the Li-Milner Structure Theorem. Major topics covered include chains and antichains, lowest upper and greatest lower bounds, retractions, algorithmic approaches, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, and the role of algebraic topology. This new edition shifts the primary focus to finite ordered sets, with results on infinite ordered sets presented toward the end of each chapter whenever possible. Also new are Chapter 6 on graphs and homomorphisms, which serves to separate the fixed clique property from the more fundamental fixed simplex property as well as to discuss the connections and differences between graph homomorphisms and order-preserving maps, and an appendix on discrete Morse functions and their use for the fixed point property for ordered sets.
Rich in examples, diagrams, and exercises, the second edition of Ordered Sets will be an excellent text for undergraduate and graduate students and a valuable resource for interested researchers. It will be especially useful to those looking for an introduction to the theory of ordered sets and its connections to such areas as algebraic topology, analysis, and computer science.
¿¿A gem. Undergraduate mathematics and computer science majors will find the first chapters offering background that will serve them well in many courses. The rest of the book, which features many open problems, constitutes an accessible and stimulating invitation to research . . . Highly recommended."
¿ CHOICE
¿The author presents the field of ordered sets in an attractive way and the many open problems presented in the book are invaluable...[T]he book is a success, it presents an in depth and up to date carefully written coverage of ordered sets." ¿SIGACT NEWS<
A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's, and Hashimoto's Theorems to more recent results such as the Li-Milner Structure Theorem. Major topics covered include chains and antichains, lowest upper and greatest lower bounds, retractions, algorithmic approaches, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, and the role of algebraic topology. This new edition shifts the primary focus to finite ordered sets, with results on infinite ordered sets presented toward the end of each chapter whenever possible. Also new are Chapter 6 on graphs and homomorphisms, which serves to separate the fixed clique property from the more fundamental fixed simplex property as well as to discuss the connections and differences between graph homomorphisms and order-preserving maps, and an appendix on discrete Morse functions and their use for the fixed point property for ordered sets.
Rich in examples, diagrams, and exercises, the second edition of Ordered Sets will be an excellent text for undergraduate and graduate students and a valuable resource for interested researchers. It will be especially useful to those looking for an introduction to the theory of ordered sets and its connections to such areas as algebraic topology, analysis, and computer science.
¿¿A gem. Undergraduate mathematics and computer science majors will find the first chapters offering background that will serve them well in many courses. The rest of the book, which features many open problems, constitutes an accessible and stimulating invitation to research . . . Highly recommended."
¿ CHOICE
¿The author presents the field of ordered sets in an attractive way and the many open problems presented in the book are invaluable...[T]he book is a success, it presents an in depth and up to date carefully written coverage of ordered sets." ¿SIGACT NEWS<
Presents a wide range of material, from classical to brand new results
Uses a modular presentation in which core material is kept brief, allowing for a broad exposure to the subject without overwhelming readers with too much information all at once
Introduces topics by examining how they related to research problems, providing continuity among diverse topics and encouraging readers to explore these problems with research of their own
Includes supplementary material: [...]
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.
Erscheinungsjahr: | 2016 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
xvi
420 S. 43 s/w Illustr. 10 farbige Illustr. 420 p. 53 illus. 10 illus. in color. |
ISBN-13: | 9783319297866 |
ISBN-10: | 3319297864 |
Sprache: | Englisch |
Herstellernummer: | 978-3-319-29786-6 |
Einband: | Gebunden |
Autor: | Schröder, Bernd |
Auflage: | 2nd edition 2016 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 28 mm |
Von/Mit: | Bernd Schröder |
Erscheinungsdatum: | 20.05.2016 |
Gewicht: | 0,896 kg |
Presents a wide range of material, from classical to brand new results
Uses a modular presentation in which core material is kept brief, allowing for a broad exposure to the subject without overwhelming readers with too much information all at once
Introduces topics by examining how they related to research problems, providing continuity among diverse topics and encouraging readers to explore these problems with research of their own
Includes supplementary material: [...]
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.
Erscheinungsjahr: | 2016 |
---|---|
Fachbereich: | Arithmetik & Algebra |
Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
Rubrik: | Naturwissenschaften & Technik |
Medium: | Buch |
Inhalt: |
xvi
420 S. 43 s/w Illustr. 10 farbige Illustr. 420 p. 53 illus. 10 illus. in color. |
ISBN-13: | 9783319297866 |
ISBN-10: | 3319297864 |
Sprache: | Englisch |
Herstellernummer: | 978-3-319-29786-6 |
Einband: | Gebunden |
Autor: | Schröder, Bernd |
Auflage: | 2nd edition 2016 |
Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
Verantwortliche Person für die EU: | Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com |
Maße: | 241 x 160 x 28 mm |
Von/Mit: | Bernd Schröder |
Erscheinungsdatum: | 20.05.2016 |
Gewicht: | 0,896 kg |