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The Resource Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource)

Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource)

Label
Ordered Sets : An Introduction with Connections from Combinatorics to Topology
Title
Ordered Sets
Title remainder
An Introduction with Connections from Combinatorics to Topology
Statement of responsibility
by Bernd Schröder
Creator
Subject
Language
eng
Summary
The second edition of this highly praised textbook provides an expanded introduction to the theory of ordered sets and its connections to various subjects. Utilizing a modular presentation, the core material is purposely kept brief, allowing for the benefits of a broad exposure to the subject without the risk of overloading the reader with too much information all at once. The remaining chapters can then be read in almost any order, giving the text a greater depth and flexibility of use. Most topics are introduced by examining how they relate to research problems, some of them still open, allowing for continuity among diverse topics and encouraging readers to explore these problems further with research of their own. 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. PRAISE FOR THE FIRST EDITION "The author has done the field a service by producing an excellent text strong in the presentation of certain topological aspects of the underlying diagrams, e.g., which should serve the developing community and field well and which can be recommended without reservations as one of the volumes which should grace a poseteer's library whether she is interested only or mainly in the theory of these objects or has directed her gaze towards applications. As a sourcebook of ideas and understanding it will make its mark. And deservedly so." ✹ZENTRALBLATT MATH "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--
Member of
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Schröder, Bernd
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/subjectName
  • Mathematics
  • Algebra
  • Ordered algebraic structures
  • Mathematical logic
  • Algebraic topology
  • Combinatorics
Label
Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-29788-0
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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 PQ̂ = Hom (Q, P) and Products -- Enumeration of Ordered Sets -- Appendix A: Some Algebraic Topology -- Appendix B: Some Discrete Morse Theory -- References -- Index
Control code
978-3-319-29788-0
Dimensions
unknown
Edition
2nd ed. 2016.
Extent
1 online resource (xvi, 420 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319297880
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-29788-0
Other physical details
53 illustrations, 10 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)950260666
Label
Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-29788-0
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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 PQ̂ = Hom (Q, P) and Products -- Enumeration of Ordered Sets -- Appendix A: Some Algebraic Topology -- Appendix B: Some Discrete Morse Theory -- References -- Index
Control code
978-3-319-29788-0
Dimensions
unknown
Edition
2nd ed. 2016.
Extent
1 online resource (xvi, 420 pages)
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319297880
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-29788-0
Other physical details
53 illustrations, 10 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)950260666

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