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الصفحة 1
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Algorithms in Invariant Theory
The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions.
Algorithms and Programming : Problems and Solutions
This book containing classical and well-known problems supplemented by clear and in-depth explanations. The material covered includes such topics as combinatorics, sorting, searching, queues, grammar and parsing, selected well-known algorithms and much more.
Algorithms – ESA 2005 ; 13th Annual European Symposium, Palma de Mallorca, Spain, October 3-6, 2005, Proceedings
This volume contains the 75 contributed papers and the abstracts of the threeinvited lectures presented at the 13th Annual European Symposium on Algo-rithms (ESA 2005), held in Spain, 2005. respectively.Papers were solicited in all areas of algorithmic research, including but notlimited to algorithmic aspects of networks, approximation and on-line algo-rithms, computational biology, computational geometry, computational financeand algorithmic game theory, data structures, database and information re-trieval, external memory algorithms, graph algorithms, graph drawing, machinelearning, mobile computing, pattern matching and data compression, quantumcomputing, and randomized algorithms. The algorithms could be sequential,distributed, or parallel. Submissions were especially encouraged in the area ofmathematical programming and operations research, including combinatorialoptimization, integer programming, polyhedral combinatorics, and semidefiniteprogramming.Each extended abstract was submitted to one of the two tracks.
Lectures on Advances in Combinatorics
The main focus of these lectures is basis extremal problems and inequalities – two sides of the same coin. Additionally they prepare well for approaches and methods useful and applicable in a broader mathematical context. Highlights of the book include a solution to the famous 4m-conjecture of Erdös/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of Erdös (1962) in combinatorial number theory "What is the maximal cardinality of a set of numbers smaller than n with no k+1 of its members pair wise relatively prime?", and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality.
Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.
Classification Algorithms for Codes and Designs
Almost a century earlier, in 1782, Euler [180] published some results on classifying small Latin squares, but for the ?rst few steps in this direction one should actually go at least as far back as ancient Greece and the proof that there are exactly ?ve Platonic solids. One of the most remarkable achievements in the early, pre-computer era is the classi?cation of the Steiner triple systems of order 15, quoted above. An onerous task that, today, no sensible person would attempt by hand calcu- tion. Because, with the exception of occasional parameters for which com- natorial arguments are e?ective (often to prove nonexistence or uniqueness), classi?cation in general is about algorithms and computation.
An Introduction to Sequential Dynamical Systems
This text is the first to provide a comprehensive introduction to SDS. Driven by numerous examples and thought-provoking problems, the presentation offers good foundational material on finite discrete dynamical systems which leads systematically to an introduction of SDS. Techniques from combinatorics, algebra and graph theory are used to study a broad range of topics, including reversibility, the structure of fixed points and periodic orbits, equivalence, morphisms and reduction. Unlike other books that concentrate on determining the structure of various networks, this book investigates the dynamics over these networks by focusing on how the underlying graph structure influences the properties of the associated dynamical system.
Algebraic Combinatorics : Lectures at a Summer School in Nordfjordeid, Norway, June 2003
This book is based on two series of lectures given at a summer school on algebraic combinatorics at the Sophus Lie Centre in Nordfjordeid, Norway, in June 2003, one by Peter Orlik on hyperplane arrangements, and the other one by Volkmar Welker on free resolutions.
