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)
Resource Information
The item Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 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 LiMilner 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 orderpreserving 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
 Language
 eng
 Edition
 2nd ed. 2016.
 Extent
 1 online resource (xvi, 420 pages)
 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
 Isbn
 9783319297880
 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
 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 LiMilner 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 orderpreserving 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
 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)
 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
 9783319297880
 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, noncommercial 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
 10.1007/9783319297880
 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)
 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
 9783319297880
 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, noncommercial 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
 10.1007/9783319297880
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/OrderedSetsAnIntroductionwithConnections/MDI0xSFbQ8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/OrderedSetsAnIntroductionwithConnections/MDI0xSFbQ8/">Ordered Sets : An Introduction with Connections from Combinatorics to Topology, by Bernd Schröder, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>