Finite Ordered Sets

Author : Nathalie Caspard,Bruno Leclerc,Bernard Monjardet
Publisher : Cambridge University Press
Page : 351 pages
File Size : 52,7 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781107080003

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Finite Ordered Sets by Nathalie Caspard,Bruno Leclerc,Bernard Monjardet Pdf

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.

Author : David Arnold
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 53,6 Mb
Release : 2012-11-14
Category : Mathematics
ISBN : 9781441987501

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Abelian Groups and Representations of Finite Partially Ordered Sets by David Arnold Pdf

The theme of this book is an exposition of connections between representations of finite partially ordered sets and abelian groups. Emphasis is placed throughout on classification, a description of the objects up to isomorphism, and computation of representation type, a measure of when classification is feasible. David M. Arnold is the Ralph and Jean Storm Professor of Mathematics at Baylor University. He is the author of "Finite Rank Torsion Free Abelian Groups and Rings" published in the Springer-Verlag Lecture Notes in Mathematics series, a co-editor for two volumes of conference proceedings, and the author of numerous articles in mathematical research journals.

Author : Bernd Schröder
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200536

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Ordered Sets by Bernd Schröder Pdf

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Author : Egbert Harzheim
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 43,8 Mb
Release : 2005-02-17
Category : Mathematics
ISBN : 9780387242194

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Ordered Sets by Egbert Harzheim Pdf

The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory.

Author : Lothar Budach
Publisher : Unknown
Page : 172 pages
File Size : 53,5 Mb
Release : 1988
Category : Algebra, Homological
ISBN : UOM:39015046279561

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Algebraic and Topological Properties of Finite Partially Ordered Sets by Lothar Budach Pdf

Author : Ivan Rival
Publisher : Springer Science & Business Media
Page : 963 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789400977983

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Ordered Sets by Ivan Rival Pdf

This volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice theoretic methods would lead to solutions of important problems in group theory.

Author : Ian Anderson
Publisher : Courier Corporation
Page : 276 pages
File Size : 52,5 Mb
Release : 2012-04-30
Category : Mathematics
ISBN : 9780486143712

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Combinatorics of Finite Sets by Ian Anderson Pdf

Coherent treatment provides comprehensive view of basic methods and results of the combinatorial study of finite set systems. The Clements-Lindstrom extension of the Kruskal-Katona theorem to multisets is explored, as is the Greene-Kleitman result concerning k-saturated chain partitions of general partially ordered sets. Connections with Dilworth's theorem, the marriage problem, and probability are also discussed. Each chapter ends with a helpful series of exercises and outline solutions appear at the end. "An excellent text for a topics course in discrete mathematics." — Bulletin of the American Mathematical Society.

Author : Ian Anderson
Publisher : Courier Corporation
Page : 276 pages
File Size : 42,8 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0486422577

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Combinatorics of Finite Sets by Ian Anderson Pdf

Among other subjects explored are the Clements-Lindström extension of the Kruskal-Katona theorem to multisets and the Greene-Kleitmen result concerning k-saturated chain partitions of general partially ordered sets. Includes exercises and solutions.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 262 pages
File Size : 48,9 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 0821895885

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Ordered Sets and Lattices II by Anonim Pdf

This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.

Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 54,5 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 3540225250

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Theory of Sets by N. Bourbaki Pdf

This is a softcover reprint of the English translation of 1968 of N. Bourbaki's, Théorie des Ensembles (1970).

Author : Norbert W Sauer,R.E. Woodrow,B. Sands
Publisher : Springer Science & Business Media
Page : 452 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401120807

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Finite and Infinite Combinatorics in Sets and Logic by Norbert W Sauer,R.E. Woodrow,B. Sands Pdf

This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.

Author : Daniel Simson
Publisher : CRC Press
Page : 516 pages
File Size : 45,9 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 2881248284

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Linear Representations of Partially Ordered Sets and Vector Space Categories by Daniel Simson Pdf

This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.

Author : William Henry Young,Grace Chisholm Young
Publisher : CUP Archive
Page : 336 pages
File Size : 48,8 Mb
Release : 1972
Category : Mathematics
ISBN : 8210379456XXX

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The Theory of Sets of Points by William Henry Young,Grace Chisholm Young Pdf

From the Preface to the First Edition (1906): ``There are no definitely accepted landmarks in the didactic treatment of Georg Cantor's magnificent theory, which is the subject of the present volume. A few of the most modern books on the Theory of Functions devote some pages to the establishment of certain results belonging to our subject, and required for the special purposes in hand ... But we may fairly claim that the present work is the first attempt at a systematic exposition of the subject as a whole.'' In this second edition, notes have been added by I. Grattan-Guinness drawn from extensive annotations in the author's own copy. A further appendix has been added.

Author : Daniel Gerbner,Balazs Patkos
Publisher : CRC Press
Page : 269 pages
File Size : 55,8 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9780429804113

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Extremal Finite Set Theory by Daniel Gerbner,Balazs Patkos Pdf

Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.

Author : Hartmut Ehrig
Publisher : Springer Science & Business Media
Page : 495 pages
File Size : 47,8 Mb
Release : 2001-12-14
Category : Computers
ISBN : 9783540430674

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Unifying Petri Nets by Hartmut Ehrig Pdf

Since their introduction nearly 40 years ago, research on Petri nets has diverged in many different directions. Various classes of Petri net, motivated either by theory or applications, with its own specific features and methods of analysis, have been proposed and studies in depth. These successful developments have led to a very heterogeneous landscape of diverse models, and this, in turn, has stimulated research on concepts and approaches that contribute to unifying and structuring the diverse landscape. This state-of-the-art survey presents the most relevant approaches to unifying Petri nets in a systematic and coherent way. The 14 chapters written by leading researchers are organized in topical sections on application-oriented approaches, unifying frameworks, and theoretical approaches.