Products related to Combinatorial:
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Combinatorial Mathematics
This long-awaited textbook is the most comprehensive introduction to a broad swath of combinatorial and discrete mathematics.The text covers enumeration, graphs, sets, and methods, and it includes both classical results and more recent developments.Assuming no prior exposure to combinatorics, it explains the basic material for graduate-level students in mathematics and computer science.Optional more advanced material also makes it valuable as a research reference.Suitable for a one-year course or a one-semester introduction, this textbook prepares students to move on to more advanced material.It is organized to emphasize connections among the topics, and facilitate instruction, self-study, and research, with more than 2200 exercises (many accompanied by hints) at various levels of difficulty.Consistent notation and terminology are used throughout, allowing for a discussion of diverse topics in a unified language.The thorough bibliography, containing thousands of citations, makes this a valuable source for students and researchers alike.
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Introduction to Combinatorial Optimization
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields.There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems.Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization.Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, suchas greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer.Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
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Introduction to Combinatorial Optimization
Introductory courses in combinatorial optimization are popular at the upper undergraduate/graduate levels in computer science, industrial engineering, and business management/OR, owed to its wide applications in these fields.There are several published textbooks that treat this course and the authors have used many of them in their own teaching experiences. This present text fills a gap and is organized with a stress on methodology and relevant content, providing a step-by-step approach for the student to become proficient in solving combinatorial optimization problems.Applications and problems are considered via recent technology developments including wireless communication, cloud computing, social networks, and machine learning, to name several, and the reader is led to the frontiers of combinatorial optimization.Each chapter presents common problems, such as minimum spanning tree, shortest path, maximum matching, network flow, set-cover, as well as key algorithms, suchas greedy algorithm, dynamic programming, augmenting path, and divide-and-conquer.Historical notes, ample exercises in every chapter, strategically placed graphics, and an extensive bibliography are amongst the gems of this textbook.
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Combinatorial Optimization : Algorithms and Complexity
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Combinatorial Problems In Mathematical Competitions
This book focuses on combinatorial problems in mathematical competitions.It provides basic knowledge on how to solve combinatorial problems in mathematical competitions, and also introduces important solutions to combinatorial problems and some typical problems with often-used solutions.Some enlightening and novel examples and exercises are well chosen in this book.With this book, readers can explore, analyze and summarize the ideas and methods of solving combinatorial problems.Their mathematical culture and ability will be improved remarkably after reading this book.
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Topics Surrounding the Combinatorial Anabelian Geometry of Hyperbolic Curves II : Tripods and Combinatorial Cuspidalization
The present monograph further develops the study, via the techniques of combinatorial anabelian geometry, of the profinite fundamental groups of configuration spaces associated to hyperbolic curves over algebraically closed fields of characteristic zero. The starting point of the theory of the present monograph is a combinatorial anabelian result which allows one to reduce issues concerning the anabelian geometry of configuration spaces to issues concerning the anabelian geometry of hyperbolic curves, as well as to give purely group-theoretic characterizations of the cuspidal inertia subgroups of one-dimensional subquotients of the profinite fundamental group of a configuration space. We then turn to the study of tripod synchronization, i.e., of the phenomenon that an outer automorphism of the profinite fundamental group of a log configuration space associated to a stable log curve inducesthe same outer automorphism on certain subquotients of such a fundamental group determined by tripods [i.e., copies of the projective line minus three points].The theory of tripod synchronization shows that such outer automorphisms exhibit somewhat different behavior from the behavior that occurs in the case of discrete fundamental groups and, moreover, may be applied to obtain various strong results concerning profinite Dehn multi-twists. In the final portion of the monograph, we develop a theory of localizability, on the dual graph of a stable log curve, for the condition that an outer automorphism of the profinite fundamental group of the stable log curve lift to an outer automorphism of the profinite fundamental group of a corresponding log configuration space.This localizability is combined with the theory of tripod synchronization to construct a purely combinatorial analogue of the natural outer surjection from the étale fundamental group of the moduli stack of hyperbolic curves over the field of rational numbers to the absolute Galois group of the field of rational numbers.
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Combinatorial Algorithms : Generation, Enumeration, and Search
This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search.Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:Combinations Permutations Graphs Designs Many classical areas are covered as well as new research topics not included in most existing texts, such as: Group algorithms Graph isomorphism Hill-climbing Heuristic search algorithms This work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area.The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
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Combinatorial Models for Scheduling Sports Tournaments
This book introduces solutions for sports scheduling problems in a variety of settings.In particular the book covers timetabling, the traveling tournament problem, carryover minimization, breaks minimization, tournament design, tournament planning, and referee assignment.A rich selection of applications to sports such as football, baseball, basketball, cricket or hockey are employed to illustrate the methods and techniques.In a step-by-step tutorial format the book describes the use of graph theory concepts, local search operators and integer programming in the context of sports scheduling.The methods presented in this book are essential to sports scheduling in all its dimensions, from tournaments that are followed by millions of people across the world, with broadcast rights that amount to hundreds of millions of dollars in some competitions, to amateur leagues that require coordination and logistical efforts due to the large number of tournaments and competitors.
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Similar search terms for Combinatorial:
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What is the difference between combinatorial arrangement and combinatorial disorder?
Combinatorial arrangement refers to the organized and systematic way in which elements are arranged or combined to form a specific structure or pattern, such as in a permutation or combination. On the other hand, combinatorial disorder refers to the lack of organization or pattern in the arrangement of elements, resulting in a random or chaotic distribution. In other words, combinatorial arrangement involves a deliberate and structured arrangement of elements, while combinatorial disorder involves a lack of structure or organization.
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What is a combinatorial problem?
A combinatorial problem is a type of mathematical problem that involves counting, arranging, or selecting objects according to specific rules or constraints. These problems often involve finding the number of possible combinations, permutations, or arrangements of a given set of elements. Combinatorial problems can arise in various fields such as computer science, probability, and optimization, and they are often solved using techniques from combinatorics, a branch of mathematics that deals with counting and arranging objects.
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What is the combinatorial sequence?
The combinatorial sequence is a sequence of numbers that represents the number of ways to choose or arrange a certain number of elements from a set. It is often used in mathematics and computer science to solve problems related to counting and arranging objects. Combinatorial sequences can be used to calculate permutations, combinations, and other arrangements of objects, and they are an important tool in solving problems related to probability, statistics, and discrete mathematics.
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Do you have difficulty with combinatorial tasks?
As an AI, I do not have difficulty with combinatorial tasks. I am designed to efficiently process and analyze large amounts of data to provide accurate and relevant information. Combinatorial tasks involve exploring different combinations and possibilities, which is something I can handle effectively. My computational capabilities allow me to quickly generate and evaluate various combinations to find the most optimal solutions.
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Can you give me some combinatorial problems?
Sure! Here are a few combinatorial problems you can try: 1. How many different ways can you arrange the letters in the word "COMBINATORIAL"? 2. In how many ways can you choose a committee of 3 people from a group of 10? 3. If you have 5 different flavors of ice cream and want to try 3 different flavors, how many different combinations of flavors can you choose? 4. How many different 4-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition? 5. In how many ways can you arrange 6 books on a shelf if 2 of the books must always be together? These problems involve counting and arranging objects in different ways, which are common themes in combinatorics.
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Do you have difficulties with combinatorial tasks?
As an AI, I do not have difficulties with combinatorial tasks. I am designed to efficiently process and analyze large amounts of data to provide accurate and relevant information. Combinatorial tasks involve exploring different combinations and permutations, which can be challenging for humans due to limitations in processing power and memory capacity. However, I can handle these tasks with ease and precision.
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Can you help me with combinatorial counting?
Yes, I can help you with combinatorial counting. Combinatorial counting involves counting the number of ways to arrange or select items from a set, and it is a fundamental concept in combinatorics. I can assist you in understanding the basic principles of combinatorial counting, such as permutations, combinations, and the use of factorial notation. Additionally, I can provide examples and step-by-step explanations to help you grasp the concepts and solve problems related to combinatorial counting.
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What is a combinatorial problem in statistics?
A combinatorial problem in statistics involves counting the number of ways that a certain event or combination of events can occur. This type of problem often arises when dealing with permutations, combinations, or arrangements of objects or events. Combinatorial problems are important in statistics because they help to determine the likelihood of certain outcomes and can be used to calculate probabilities and make predictions. These problems are often solved using techniques from combinatorics, such as factorial notation, combinations, and permutations.
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