Independence Theory In Combinatorics
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Independence Theory In Combinatorics
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Author : V. Bryant
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Independence Theory In Combinatorics written by V. Bryant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Combinatorics may very loosely be described as that branch of mathematics which is concerned with the problems of arranging objects in accordance with various imposed constraints. It covers a wide range of ideas and because of its fundamental nature it has applications throughout mathematics. Among the well-established areas of combinatorics may now be included the studies of graphs and networks, block designs, games, transversals, and enumeration problem s concerning permutations and combinations, from which the subject earned its title, as weil as the theory of independence spaces (or matroids). Along this broad front,various central themes link together the very diverse ideas. The theme which we introduce in this book is that of the abstract concept of independence. Here the reason for the abstraction is to unify; and, as we sh all see, this unification pays off handsomely with applications and illuminating sidelights in a wide variety of combinatorial situations. The study of combinatorics in general, and independence theory in particular, accounts for a considerable amount of space in the mathematical journais. For the most part, however, the books on abstract independence so far written are at an advanced level, ·whereas the purpose of our short book is to provide an elementary in troduction to the subject.
Independence Theory In Combinatorics
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Author : V. Bryant
language : en
Publisher:
Release Date : 1980-10-02
Independence Theory In Combinatorics written by V. Bryant and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-10-02 with categories.
Set Theory An Introduction To Independence Proofs
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Author : K. Kunen
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Set Theory An Introduction To Independence Proofs written by K. Kunen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.
Set Theory
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Author : Kenneth Kunen
language : en
Publisher:
Release Date : 2006
Set Theory written by Kenneth Kunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Axiomatic set theory categories.
"Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory" -- Provided by publisher.
Introduction To Algebraic Independence Theory
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Author : Yuri V. Nesterenko
language : en
Publisher:
Release Date : 2014-01-15
Introduction To Algebraic Independence Theory written by Yuri V. Nesterenko and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Introduction To Algebraic Independence Theory
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Author : Yuri V. Nesterenko
language : en
Publisher: Springer
Release Date : 2003-07-01
Introduction To Algebraic Independence Theory written by Yuri V. Nesterenko and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.
Set Theory
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Author : Ralf Schindler
language : en
Publisher: Springer
Release Date : 2014-05-22
Set Theory written by Ralf Schindler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with Mathematics categories.
This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.
Transversal Theory
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Author : L. Mirsky
language : en
Publisher: Academic Press
Release Date : 1971-04-20
Transversal Theory written by L. Mirsky and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-04-20 with Computers categories.
Transversal Theory
Topics In Matroid Theory
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Author : Leonidas S. Pitsoulis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-24
Topics In Matroid Theory written by Leonidas S. Pitsoulis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-24 with Mathematics categories.
Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.
Combinatorial Optimization
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Author : Bernhard Korte
language : en
Publisher: Springer
Release Date : 2018-03-13
Combinatorial Optimization written by Bernhard Korte and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Mathematics categories.
This comprehensive textbook on combinatorial optimization places special emphasis on theoretical results and algorithms with provably good performance, in contrast to heuristics. It is based on numerous courses on combinatorial optimization and specialized topics, mostly at graduate level. This book reviews the fundamentals, covers the classical topics (paths, flows, matching, matroids, NP-completeness, approximation algorithms) in detail, and proceeds to advanced and recent topics, some of which have not appeared in a textbook before. Throughout, it contains complete but concise proofs, and also provides numerous exercises and references. This sixth edition has again been updated, revised, and significantly extended. Among other additions, there are new sections on shallow-light trees, submodular function maximization, smoothed analysis of the knapsack problem, the (ln 4+ɛ)-approximation for Steiner trees, and the VPN theorem. Thus, this book continues to represent the state of the art of combinatorial optimization.