Counting And Configurations
Download Counting And Configurations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Counting And Configurations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages.
Counting and Configurations
Author: Jiri Herman
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
This book can be seen as a continuation of Equations and Inequalities: El ementary Problems and Theorems in Algebra and Number Theory by the same authors, and published as the first volume in this book series. How ever, it can be independently read or used as a textbook in its own right. This book is intended as a text for a problem-solving course at the first or second-year university level, as a text for enrichment classes for talented high-school students, or for mathematics competition training. It can also be used as a source of supplementary material for any course dealing with combinatorics, graph theory, number theory, or geometry, or for any of the discrete mathematics courses that are offered at most American and Canadian universities. The underlying "philosophy" of this book is the same as that of Equations and Inequalities. The following paragraphs are therefore taken from the preface of that book.
Principles of Combinatorics
Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.
Techniques of Counting
"Techniques of Counting" "Techniques of Counting" is a comprehensive and authoritative guide that delves deeply into the art and science of enumeration, a cornerstone of combinatorics and discrete mathematics. The book commences with a meticulous treatment of fundamental counting principles—such as the sum and product rules, permutations, combinations, and critical axioms like the pigeonhole principle and inclusion-exclusion. Through crisp exposition and illustrative examples, the early chapters lay a robust groundwork, equipping readers with the essential tools needed for both elementary and intricate counting scenarios, all while seamlessly connecting to the broader framework of set theory and combinatorial identities. Building on this foundation, the text skillfully navigates advanced topics including generating functions, recurrence relations, and a rich array of combinatorial structures such as multinomials, Stirling and Bell numbers, Catalan numbers, and Ferrers diagrams. It ventures further into specialized domains, providing thorough coverage of graph enumeration, group-theoretic methods, and analytic tools like asymptotics and singularity analysis. Readers are introduced to elegant algebraic techniques, probabilistic methods, and the challenges of counting within complexity theory, with dedicated chapters on the computational hardness of counting problems, approximate algorithms, and the subtleties of constraint-based enumeration. The final chapters broaden the book’s relevance by surveying real-world applications across diverse fields. These range from error-correcting codes and cryptographic protocols to statistical mechanics, bioinformatics, and machine learning, illustrating the versatility and profound utility of combinatorial enumeration in both theory and practice. Whether for students eager to master foundational techniques or researchers seeking advanced insights, "Techniques of Counting" stands as an indispensable reference—a lucid and exhaustive resource for anyone fascinated by the universe of counting.