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Author: Joshua Adam Gray Publisher: ISBN: Category : Languages : en Pages : 96
Book Description
Two elements e and f in a matroid M are clones if and only if the mapping that interchanges e and f and fixes all other elements of M is an automorphism. In this dissertation, we have associated clone sets in representable matroids to arcs in projective spaces Chapter One gives a survey of basic topics in matroids and results on clone sets. In Chapter Two we give definitions of projective spaces and arcs and a survey of bounds on arc sizes. In Chapter Three we improve the bound on the size of a clone set in a 3-connected [Special characters omitted.] F -representable matroid using known bounds on the size of arcs in projective spaces. Furthermore in Chapter Four we extend a result of Reid and Zhou on clone sets in 3-connected matroids to clone sets in n -connected matroids and associate the representability of an n -connected matroid with a clone set of a specified size to the representability of a similar class of matroids. Using this result, we have used similar techniques to those in Chapter Three to obtain some preliminary bounds on the size of a clone set in an n -connected [Special characters omitted.] F -representable matroid and establish a conjecture on the size of a clone set in an n -connected [Special characters omitted.] F -representable matroid.
Author: Joshua Adam Gray Publisher: ISBN: Category : Languages : en Pages : 96
Book Description
Two elements e and f in a matroid M are clones if and only if the mapping that interchanges e and f and fixes all other elements of M is an automorphism. In this dissertation, we have associated clone sets in representable matroids to arcs in projective spaces Chapter One gives a survey of basic topics in matroids and results on clone sets. In Chapter Two we give definitions of projective spaces and arcs and a survey of bounds on arc sizes. In Chapter Three we improve the bound on the size of a clone set in a 3-connected [Special characters omitted.] F -representable matroid using known bounds on the size of arcs in projective spaces. Furthermore in Chapter Four we extend a result of Reid and Zhou on clone sets in 3-connected matroids to clone sets in n -connected matroids and associate the representability of an n -connected matroid with a clone set of a specified size to the representability of a similar class of matroids. Using this result, we have used similar techniques to those in Chapter Three to obtain some preliminary bounds on the size of a clone set in an n -connected [Special characters omitted.] F -representable matroid and establish a conjecture on the size of a clone set in an n -connected [Special characters omitted.] F -representable matroid.
Author: Geoffrey Grimmett Publisher: Cambridge University Press ISBN: 1108542999 Category : Mathematics Languages : en Pages : 279
Book Description
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author: Ulle Endriss Publisher: Lulu.com ISBN: 1326912097 Category : Computers Languages : en Pages : 424
Book Description
Computational social choice is concerned with the design and analysis of methods for collective decision making. It is a research area that is located at the interface of computer science and economics. The central question studied in computational social choice is that of how best to aggregate the individual points of view of several agents, so as to arrive at a reasonable compromise. Examples include tallying the votes cast in an election, aggregating the professional opinions of several experts, and finding a fair manner of dividing a set of resources amongst the members of a group -- Back cover.
Author: Geoffrey Grimmett Publisher: Cambridge University Press ISBN: 9780521147354 Category : Mathematics Languages : en Pages : 260
Book Description
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm-Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author: Joseph L. Taylor Publisher: American Mathematical Soc. ISBN: 0821869019 Category : Functions of complex variables Languages : en Pages : 319
Book Description
"The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem." -- Publisher.
Author: George Polya Publisher: Springer Science & Business Media ISBN: 1475711018 Category : Science Languages : en Pages : 202
Book Description
In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.
Author: Murat Köksalan Publisher: Springer Science & Business Media ISBN: 3642566804 Category : Business & Economics Languages : en Pages : 478
Book Description
This volume contains a collection of papers presented at the 15th International Conference on Multiple Criteria Decision Making held in Ankara, Turkey July 10 14, 2000. This was one of the regular conferences of the International Society on Multiple Criteria Decision Making, which are held at approximately two-year intervals. The Ankara conference had 195 participants from 38 countries. A total of 185 papers were presented at the conference. The title of our volume is MCDM in the New Millennium. The papers presented at the conference reflect the theme. We had several papers on information technology (IT) and many application papers. Of the 81 application papers presented, 14 appear in the volume. We expect more IT applications of MCDM to appear in the future, in particular in the areas of e-commerce and the internet. The conference surroundings and accomodations were excellent, and conducive to both an outstanding academic exchange, and enjoyment and a cultural broadening of participants. We had a pleasant and enjoyable outing and visit to the Anatolian Civilizations Museum. We also had an outstanding banquet at which awards were presented. The MCDM Gold Medal was presented to Professor Thomas Saaty, of the University of Pittsburgh. The MCDM Presidential Service Award was presented to ProfessorPekka Korhonen of the Helsinki School of Economics for his years of presidential service to the society. The society presented the MCDM Edgeworth-Pareto Award to Professor Alexander V. Lotov of the Russian Academy of Sciences.
Author: W. Cary Huffman Publisher: CRC Press ISBN: 1351375105 Category : Computers Languages : en Pages : 998
Book Description
Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry. Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references. The book is divided into three parts: Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography. Features Suitable for students and researchers in a wide range of mathematical disciplines Contains many examples and references Most topics take the reader to the frontiers of research
Author: Joshua Adam Gray
Author: Joshua Adam Gray
Author: Geoffrey Grimmett
Author: Richard P. Stanley
Author: Robert E. Bixby
Author: Ulle Endriss
Author: Geoffrey Grimmett
Author: Joseph L. Taylor
Author: George Polya
Author: Murat Köksalan
Author: W. Cary Huffman