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Combinatorial Theory

'Classics in Mathematics (CIM)'. Reprint of the 1st ed. Berlin Heidelberg New York 1979. Book. Sprache:…
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From the reviews:"This book presents a very good introduc- tion to combinatorics. It covers most aspects of enumeration and order theory,... It is divided into three parts. The first part presents the basic material on mappings and po- sets... The se... weiterlesen
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Titel: Combinatorial Theory
Autor/en: Martin Aigner

ISBN: 3540617876
EAN: 9783540617877
'Classics in Mathematics (CIM)'.
Reprint of the 1st ed. Berlin Heidelberg New York 1979.
Book.
Sprache: Englisch.
Springer Berlin Heidelberg

16. Dezember 1996 - kartoniert - 500 Seiten

Beschreibung

From the reviews:"This book presents a very good introduc- tion to combinatorics. It covers most aspects of enumeration and order theory,... It is divided into three parts. The first part presents the basic material on mappings and po- sets... The second part deals with enumeration ... Finally the third part treats of the order-theoretic aspects ... In the text examples are given and at the end of each chapter valuable notes, also very good selected exercises. They con- stitute an organic part of the book. This book can warmly be recommended first of all to students interested in combina- torics. A two semester course can also be based on it."Publicationes Mathematicae Debrecen

Inhaltsverzeichnis

Preliminaries.- 1. Sets.- 2. Graphs.- 3. Posets.- 4. Miscellaneous Notation.- I. Mappings.- 1. Classes of Mappings.- 2. Fundamental Orders.- 3. Permutations.- 4. Patterns.- Notes.- II. Lattices.- 1. Distributive Lattices.- 2. Modular and Semimodular Lattices.- 3. Geometric Lattices.- 4. The Fundamental Examples.- Notes.- III. Counting Functions.- 1. The Elementary Counting Coefficients.- 2. Recursion and Inversion.- 3. Binomial Sequences.- 4. Order Functions.- Notes.- IV. Incidence Function.- 1. The Incidence Algebra.- 2. Möbius Inversion.- 3. The Möbius Function.- 4. Valuations.- Notes.- V. Generating Functions.- 1. Ordered Structures.- 2. Unordered Structures.- 3. G-patterns.- 4. G, H-patterns.- Notes.- VI. Matroids: Introduction.- 1. Fundamental Concepts.- 2. Fundamental Examples.- 3. Construction of Matroids.- 4. Duality and Connectivity.- Notes.- VII. Matroids: Further Theory.- 1. Linear Matroids.- 2. Binary Matroids.- 3. Graphic Matroids.- 4. Transversal Matroids.- Notes.- VIII. Combinatorial Order Theory.- 1. Maximum-Minimum Theorems.- 2. Transversal Theorems.- 3. Sperner Theorems.- 4. Ramsey Theorems.- Notes.- List of Symbols.

Portrait

Biography of Martin Aigner
Martin Aigner received his Ph.D. in Mathematics in 1965 from the University of Vienna. He then spent five years in the United States, the last two at the University of North Carolina at Chapel Hill where he was introduced to the combinatorial world (which he has never left since) by G. C. Rota and the late R. C. Bose. After extensive travels he returned to Europe and spent three years at the University of Tübingen with a senior fellowship of the German Science Foundation. Since 1974 he has been a Professor of Mathematics at the Free University of Berlin.Martin Aigner has published in various fields of combinatorics and graph theory and is the author of several monographs on discrete mathematics, graph theory and the theory of search.

Pressestimmen

From the reviews: "This book presents a very good introduction to combinatorics. It covers most aspects of enumeration and order theory,... It is divided into three parts. The first part presents the basic material on mappings and posets... The second part deals with enumeration ... Finally the third part treats of the order-theoretic aspects ... In the text examples are given and at the end of each chapter valuable notes, also very good selected exercises. They constitute an organic part of the book. This book can warmly be recommended first of all to students interested in combinatorics. A two semester course can also be based on it."
Publicationes Mathematicae Debrecen
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