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Books in Discrete mathematics combinatorics

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Lukasiewicz-Moisil Algebras

  • 1st Edition
  • Volume 49
  • May 13, 1991
  • V. Boicescu + 3 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 9 - 2
The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

Topics on Domination

  • 1st Edition
  • February 1, 1991
  • S.T. Hedetniemi + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 8 - 5
The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other domination-related parameters) can be computed in polynomial time.

Submodular Functions and Optimization

  • 1st Edition
  • Volume 47
  • January 24, 1991
  • S. Fujishige
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 7 - 8
The importance of submodular functions has been widely recognized in recent years in combinatorial optimization. This is the first book devoted to the exposition of the theory of submodular functions from an elementary technical level to an advanced one. A unifying view of the theory is shown by means of base polyhedra and duality for submodular and supermodular systems. Among the subjects treated are: neoflows (submodular flows, independent flows, polymatroidal flows), submodular analysis (submodular programs, duality, Lagrangian functions, principal partitions), nonlinear optimization with submodular constraints (lexicographically optimal bases, fair resource allocation). Special emphasis is placed on the constructive aspects of the theory, which lead to practical, efficient algorithms.

Latin Squares

  • 1st Edition
  • January 24, 1991
  • József Dénes + 1 more
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 6 - 1
In 1974 the editors of the present volume published a well-received book entitled ``Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written.The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

Algebraic and Structural Automata Theory

  • 1st Edition
  • Volume 44
  • January 14, 1991
  • B. Mikolajczak
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 4 - 7
Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

Combinatorial Designs

  • 1st Edition
  • Volume 42
  • October 11, 1989
  • A. Hartman
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 2 - 3
Haim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson's Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations.The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani's own latest work on Balanced Incomplete Block Designs. Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs.

Graph Theory and Combinatorics 1988

  • 1st Edition
  • Volume 43
  • July 1, 1989
  • B. Bollobás
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 3 - 0
Combinatorics has not been an established branch of mathematics for very long: the last quarter of a century has seen an explosive growth in the subject. This growth has been largely due to the doyen of combinatorialists, Paul Erdős, whose penetrating insight and insatiable curiosity has provided a huge stimulus for workers in the field. There is hardly any branch of combinatorics that has not been greatly enriched by his ideas.This volume is dedicated to Paul Erdős on the occasion of his seventy-fifth birthday.

Logic-Based Decision Support

  • 1st Edition
  • Volume 40
  • February 1, 1989
  • R.G. Jeroslow
  • English
  • eBook
    9 7 8 - 0 - 0 8 - 0 8 6 7 8 0 - 9
This monograph is based on a series of lectures given by the author at the first Advanced Research Institute on Discrete Applied Mathematics, held at Rutgers University. It emphasizes connections between the representational aspects of mixed integer programming and applied logic, as well as discussing logic-based approaches to decision support which help to create more `intelligent' systems. Dividing naturally into two parts, the first four chapters are an overview of mixed-integer programming representability techniques. This is followed by five chapters on applied logic, expert systems, logic and databases, and complexity theory. It concludes with a summary of open research issues and an attempt to extrapolate trends in this rapidly developing area.