| LIBRARY OF CONGRESS CONTROL NUMBER |
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| LC control number |
2017935975 |
| INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783319549804 |
| DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Call number |
512.81 OM ON |
| MAIN ENTRY--PERSONAL NAME |
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| Authors |
Omodeo, Eugenio G. |
| TITLE STATEMENT |
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| Title |
On sets and graphs : |
| Subtitle |
perspectives on logic and combinatorics / |
| Statement of responsibility, etc |
Eugenio G. Omodeo, Alberto Policriti, Alexandru I. Tomescu |
| PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) |
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| Place of publication |
Cham, Switzerland : |
| Publisher |
Springer, |
| Date |
2017. |
| PHYSICAL DESCRIPTION |
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| Extent |
xix, 275 p. : |
| Other Details |
ill. ; |
| Size |
24 cm. |
| CONTENTS |
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| Contents |
Introduction Part I: Basics Membership and Edge Relations Sets, Graphs, and Set Universes Part II: Graphs as Sets The Undirected Structure Underlying Sets Graphs as Transitive Sets Part III: Sets as Graphs Counting and Encoding Sets Random Generation of Sets Infinite Sets and Finite Combinatorics Appendix: Excerpts from a Referee-Checked Proof-Script |
| SUMMARY |
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| Summary |
This treatise presents an integrated perspective on the interplay of set theory and graph theory, providing an extensive selection of examples that highlight how methods from one theory can be used to better solve problems originated in the other. Features: explores the interrelationships between sets and graphs and their applications to finite combinatorics; introduces the fundamental graph-theoretical notions from the standpoint of both set theory and dyadic logic, and presents a discussion on set universes; explains how sets can conveniently model graphs, discussing set graphs and set-theoretic representations of claw-free graphs; investigates when it is convenient to represent sets by graphs, covering counting and encoding problems, the random generation of sets, and the analysis of infinite sets; presents excerpts of formal proofs concerning graphs, whose correctness was verified by means of an automated proof-assistant; contains numerous exercises, examples, definitions, problems and insight panels. |
| SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical Heading |
Set theory |
| SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical Heading |
Graph theory |
| ADDED ENTRY |
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| Name |
Policriti, Alberto |
| ADDED ENTRY |
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| Name |
Tomescu, Alexandru I. |
| ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
https://uowd.box.com/s/676cxmyhn50ppf6rd7cpopet9e2v79b1 |
| Public note |
Location Map |
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5987 |
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5430 |
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1003 |
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5989 |
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5990 |