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Combinatorial Theory Martin Aigner

Combinatorial Theory By Martin Aigner

Combinatorial Theory by Martin Aigner


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Summary

This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. . . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics. Publicationes Mathematicae Debrecen

Combinatorial Theory Summary

Combinatorial Theory by Martin Aigner

This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. . . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics. Publicationes Mathematicae Debrecen

Combinatorial Theory Reviews

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

About Martin Aigner

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 Tubingen 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.

Table of Contents

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. Moebius Inversion.- 3. The Moebius 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.

Additional information

NLS9783540617877
9783540617877
3540617876
Combinatorial Theory by Martin Aigner
New
Paperback
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
1996-12-16
483
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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