Generalized Connectivity of Graphs (SpringerBriefs in Mathematics)
by Xueliang Li and Yaping Mao
Noteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations...
Combinatorial Engineering of Decomposable Systems (Combinatorial Optimization, #2)
by M.S. Levin
Combinatorial Engineering of Decomposable Systems presents a morphological approach to the combinatorial design/synthesis of decomposable systems. Applications involve the following: design (e.g., information systems; user's interfaces; educational courses); planning (e.g., problem-solving strategies; product life cycles; investment); metaheuristics for combinatorial optimization; information retrieval; etc.
Introduction to Combinatorial Designs, Second Edition (Discrete Mathematics & Its Application)
by W. D. Wallis
Cylindric-like Algebras and Algebraic Logic (Bolyai Society Mathematical Studies, #22)
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski's quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory,...
Graph Theory (Graduate Texts in Mathematics, #244)
by Adrian Bondy and U.S.R. Murty
The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.
Information Theory and Applications II (Lecture Notes in Computer Science, #1133)
This book constitutes the refereed postworkshop proceedings of the Fourth Canadian Workshop on Information Theory, held in Lac Delage, Quebec, in May 1995. The book contains 18 revised full papers selected from 30 workshop presentations; also included are three invited contributions. The book is divided into sections on algebraic coding, cryptography and secure communications, decoding methods and techniques, coding and modulation for fading channels, and signal processing and pattern recognitio...
Theory of Coronoid Hydrocarbons II (Lecture Notes in Chemistry, #62)
by S. J. Cyvin, J. Brunvoll, R.S. Chen, B.N. Cyvin, and F.J. Zhang
The present monograph is a continuation of Cyvin SJ, Brunvoll J and Cyvin (1991c), a reference to be found in Bibliography. Naturally, the previous volume is cited frequently here. For the sake of brevity, it is referred to as "Volume I". References to different chapters, sections or paragraphs are given like Vol. 1-1, 1-1.2 or 1-1.2.2, respectively. Also tables and equations in "Volume I" are cited; the very last equation therein, for instance, is Vol. I-{9.9). The present text spans from refer...
Combinatorial Convexity and Algebraic Geometry (Graduate Texts in Mathematics, #168)
by Gunter Ewald
The book is an introduction to the theory of convex polytopes and polyhedral sets, to algebraic geometry, and to the connections between these fields, known as the theory of toric varieties. The first part of the book covers the theory of polytopes and provides large parts of the mathematical background of linear optimization and of the geometrical aspects in computer science. The second part introduces toric varieties in an elementary way.
Enumerative Combinatorics (Discrete Mathematics and Its Applications)
by Charalambos A. Charalambides
Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theore...
Infinite Dimensional Lie Algebras (Progress in Mathematics, #44)
by Victor G. Kac
This is the third, substantially revised edition of this important monograph. The book is concerned with Kac-Moody algebras, a particular class of infinite-dimensional Lie algebras, and their representations. It is based on courses given over a number of years at MIT and in Paris, and is sufficiently self-contained and detailed to be used for graduate courses. Each chapter begins with a motivating discussion and ends with a collection of exercises, with hints to the more challenging problems.
Error-Correcting Codes
by Professor and Dean of Economics and Social Studies John Baylis
This book presents a modular and expandable technique in the rapidly emerging research area of automatic configuration and selection of the best algorithm for the instance at hand. The author presents the basic model behind ISAC and then details a number of modifications and practical applications. In particular, he addresses automated feature generation, offline algorithm configuration for portfolio generation, algorithm selection, adaptive solvers, online tuning, and parallelization. The...
Scale-isometric Polytopal Graphs In Hypercubes And Cubic Lattices: Polytopes In Hypercubes And Zn
by Michel-marie Deza, Viacheslav Grishukhin, and Mikhail I Shtogrin
This monograph identifies polytopes that are "combinatorially 1-embeddable", within interesting lists of polytopal graphs, i.e. such that corresponding polytopes are either prominent mathematically (regular partitions, root lattices, uniform polytopes and so on), or applicable in chemistry (fullerenes, polycycles, etc.). The embeddability, if any, provides applications to chemical graphs and, in the first case, it gives new combinatorial perspective to " 2-prominent" affine polytopal objects.Th...
This book is a tribute to Paul Erd\H{o}s, the wandering mathematician once described as the "prince of problem solvers and the absolute monarch of problem posers." It examines -- within the context of his unique personality and lifestyle -- the legacy of open problems he left to the world after his death in 1996. Unwilling to succumb to the temptat
Graphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well...
This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains classical contents including the description of all finite-dimensional modules and an introduction to the universal enveloping algebras with its primitive ideals, alongside non-classical contents including the description of all simple weight mo...
Quadratic Forms (Algebra and Applications, #25)
by Michael Barot, Jesus Arturo Jimenez Gonzalez, and Jose Antonio De La Pena
This monograph presents combinatorial and numerical issues on integral quadratic forms as originally obtained in the context of representation theory of algebras and derived categories. Some of these beautiful results remain practically unknown to students and scholars, and are scattered in papers written between 1970 and the present day. Besides the many classical results, the book also encompasses a few new results and generalizations. The material presented will appeal to a wide group of r...
Mathematics of Program Construction (Lecture Notes in Computer Science, #947)
This volume constitutes the proceedings of the Third International Conference on the Mathematics of Program Construction, held at Kloster Irsee, Germany in July 1995. Besides five invited lectures by distinguished researchers there are presented 19 full revised papers selected from a total of 58 submissions. The general theme is the use of crisp, clear mathematics in the discovery and design of algorithms and in the development of corresponding software and hardware; among the topics addressed a...
Graph Algorithms And Applications 2
by Giuseppe Liotta, Roberto Tamassia, and Ioannis G Tollis
This book contains Volumes 4 and 5 of the Journal of Graph Algorithms and Applications (JGAA). The first book of this series, Graph Algorithms and Applications 1, published in March 2002, contains Volumes 1-3 of JGAA.JGAA is a peer-reviewed scientific journal devoted to the publication of high-quality research papers on the analysis, design, implementation, and applications of graph algorithms. Areas of interest include computational biology, computational geometry, computer graphics, computer-a...
The Simplex Method (Algorithms and Combinatorics, #1) (Texts and Monographs in Physics,, #1)
by Karl Heinz Borgwardt
For more than 35 years now, George B. Dantzig's Simplex-Method has been the most efficient mathematical tool for solving linear programming problems. It is proba bly that mathematical algorithm for which the most computation time on computers is spent. This fact explains the great interest of experts and of the public to understand the method and its efficiency. But there are linear programming problems which will not be solved by a given variant of the Simplex-Method in an acceptable time. The...
Most Perfect Pandiagonal Magic Squares
by Kathleen Ollerenshaw and David Bree
Number Theory and Combinatorics (De Gruyter Proceedings in Mathematics)
Over a career that spanned 60 years, Ronald L. Graham (known to all as Ron) made significant contributions to the fields of discrete mathematics, number theory, Ramsey theory, computational geometry, juggling and magical mathematics, and many more. Ron also was a mentor to generations of mathematicians, he gave countless talks and helped bring mathematics to a wider audience, and he held signifi cant leadership roles in the mathematical community. This volume is dedicated to the life and memo...
Integer Programming and Combinatorial Optimization (Lecture Notes in Computer Science, #1084)
This volume presents the proceedings of the Fifth Integer Programming and Combinatorial Optimization Conference, IPCO V, held in Vancouver, British Columbia, Canada, in June 1996. The 36 revised papers included in the book were selected from a total of 99 submissions; they highlight recent developments in theory, computation, and applications of integer programming and combinatorial optimization. The volume is organized in sections on integer programming theory and models, network flow algorithm...