Books in Discrete mathematics combinatorics

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Generating Functionology

• 2nd Edition
• November 17, 1993
• Herbert S. Wilf
• English
• eBook 978-0-08-057151-5

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This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter.

Combinatorial Problems and Exercises

• 2nd Edition
• August 11, 1993
• L. Lovász
• English
• eBook 978-0-08-093309-2

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The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book.Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.

Theory of Convex Structures

• 1st Edition
• Volume 50
• August 2, 1993
• M.L.J. van de Vel
• English
• eBook 978-0-08-093310-8

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Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology.Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.

Quo Vadis, Graph Theory?

• 1st Edition
• Volume 55
• March 17, 1993
• J. Gimbel + 2 more
• English
• eBook 978-0-08-086795-3

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Graph Theory (as a recognized discipline) is a relative newcomer to Mathematics. The first formal paper is found in the work of Leonhard Euler in 1736. In recent years the subject has grown so rapidly that in today's literature, graph theory papers abound with new mathematical developments and significant applications.As with any academic field, it is good to step back occasionally and ask Where is all this activity taking us?, What are the outstanding fundamental problems?, What are the next important steps to take?. In short, Quo Vadis, Graph Theory?. The contributors to this volume have together provided a comprehensive reference source for future directions and open questions in the field.

The Steiner Tree Problem

• 1st Edition
• Volume 53
• October 20, 1992
• F.K. Hwang + 2 more
• English
• eBook 978-0-08-086793-9

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The Steiner problem asks for a shortest network which spans a given set of points. Minimum spanning networks have been well-studied when all connections are required to be between the given points. The novelty of the Steiner tree problem is that new auxiliary points can be introduced between the original points so that a spanning network of all the points will be shorter than otherwise possible. These new points are called Steiner points - locating them has proved problematic and research has diverged along many different avenues.This volume is devoted to the assimilation of the rich field of intriguing analyses and the consolidation of the fragments. A section has been given to each of the three major areas of interest which have emerged. The first concerns the Euclidean Steiner Problem, historically the original Steiner tree problem proposed by Jarník and Kössler in 1934. The second deals with the Steiner Problem in Networks, which was propounded independently by Hakimi and Levin and has enjoyed the most prolific research amongst the three areas. The Rectilinear Steiner Problem, introduced by Hanan in 1965, is discussed in the third part. Additionally, a forth section has been included, with chapters discussing areas where the body of results is still emerging.The collaboration of three authors with different styles and outlooks affords individual insights within a cohesive whole.

Combinatorics '90

• 1st Edition
• Volume 52
• August 17, 1992
• A. Barlotti + 3 more
• English
• eBook 978-0-08-086792-2

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This volume forms a valuable source of information on recent developments in research in combinatorics, with special regard to the geometric point of view. Topics covered include: finite geometries (arcs, caps, special varieties in a Galois space; generalized quadrangles; Benz planes; foundation of geometry), partial geometries, Buekenhout geometries, transitive permutation sets, flat-transitive geometries, design theory, finite groups, near-rings and semifields, MV-algebras, coding theory, cryptography and graph theory in its geometric and design aspects.

Fourth Czechoslovakian Symposium on Combinatorics, Graphs and Complexity

• 1st Edition
• Volume 51
• June 26, 1992
• J. Nešetril + 1 more
• English
• eBook 978-0-08-086791-5

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This volume in the Annals of Discrete Mathematics brings together contributions by renowned researchers in combinatorics, graphs and complexity. The conference on which this book is based was the fourth in a series which began in 1963, which was the first time specialists from East and West were able to come together. The 1990 meeting attracted 170 mathematicians and computer scientists from around the world, so this book represents an international, detailed view of recent research.

Markov Processes

• 1st Edition
• October 8, 1991
• Daniel T. Gillespie
• English
• Hardback 978-0-12-283955-9

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• eBook 978-0-08-091837-2

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Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.

Truth, Possibility and Probability

• 1st Edition
• Volume 166
• June 20, 1991
• R. Chuaqui
• English
• eBook 978-0-08-087277-3

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Anyone involved in the philosophy of science is naturally drawn into the study of the foundations of probability. Different interpretations of probability, based on competing philosophical ideas, lead to different statistical techniques, and frequently to mutually contradictory consequences.This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.

Eulerian Graphs and Related Topics

• 1st Edition
• Volume 2
• June 3, 1991
• H. Fleischner
• English
• eBook 978-0-08-086790-8

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