Higher Order Combinatorics For Scholars
Download Higher Order Combinatorics For Scholars PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Higher Order Combinatorics For Scholars 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.
Higher-Order Combinatorics for Scholars
Author: Pasquale De Marco
language: en
Publisher: Pasquale De Marco
Release Date: 2025-07-10
**Higher-Order Combinatorics for Scholars** is a comprehensive introduction to higher-order combinatorics, suitable for advanced undergraduates and graduate students in mathematics, computer science, and engineering. It provides a rigorous and systematic treatment of the fundamental concepts and techniques of combinatorics, with a focus on applications to other areas of mathematics, such as graph theory, number theory, probability theory, linear algebra, optimization, complexity theory, and algorithmic combinatorics. The book is divided into ten chapters, each of which covers a different aspect of combinatorics. The first chapter introduces the basic counting principles, as well as more advanced topics such as generating functions and the inclusion-exclusion principle. The second chapter covers advanced counting techniques, such as the pigeonhole principle, Ramsey theory, and extremal combinatorics. The third chapter introduces graph theory, which is the study of graphs, which are mathematical structures that consist of a set of vertices and edges. The fourth chapter introduces set theory, which is the study of sets, which are collections of distinct objects. The fifth chapter introduces number theory, which is the study of numbers and their properties. The sixth chapter introduces probability theory, which is the study of the likelihood of events. The seventh chapter introduces linear algebra, which is the study of vectors and matrices. The eighth chapter introduces optimization, which is the study of finding the best possible solution to a given problem. The ninth chapter introduces complexity theory, which is the study of the computational resources required to solve different problems. The tenth chapter introduces algorithmic combinatorics, which is the study of algorithms for solving combinatorial problems. Each chapter contains a wealth of exercises that are designed to help the reader understand the material and to develop problem-solving skills. The book also contains a comprehensive appendix that provides a glossary of terms and a summary of important results. **Higher-Order Combinatorics for Scholars** is a valuable resource for students and researchers who are interested in combinatorics and its applications. It is also a useful reference for anyone who needs to use combinatorial techniques in their work. If you like this book, write a review!
Analytic Combinatorics
Author: Philippe Flajolet
language: en
Publisher: Cambridge University Press
Release Date: 2009-01-15
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Combinatorics and Graph Theory
Author: John Harris
language: en
Publisher: Springer Science & Business Media
Release Date: 2009-04-03
There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.