Combinatory Analysis

Combinatory Analysis
Author: Percy A. MacMahon
Publisher: Courier Corporation
Total Pages: 770
Release: 2004-07-06
Genre: Mathematics
ISBN: 9780486495866

Account of combinatory analysis theorems shows their connections and unites them as parts of a general doctrine. Topics include symmetric functions, theory of number compositions, more. 1915, 1916, and 1920 editions.

Introduction to Combinatorial Analysis

Introduction to Combinatorial Analysis
Author: John Riordan
Publisher: Courier Corporation
Total Pages: 258
Release: 2002-12-13
Genre: Mathematics
ISBN: 0486425363

Introductory text surveys the theory of permutations and combinations associated with elementary algebra; the principle of inclusion and exclusion; and the theory of distributions and partitions in cyclic representation. Includes problems. 1958 edition.

Analytic Combinatorics

Analytic Combinatorics
Author: Philippe Flajolet
Publisher: Cambridge University Press
Total Pages: 825
Release: 2009-01-15
Genre: Mathematics
ISBN: 1139477161

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.

George E. Andrews 80 Years of Combinatory Analysis

George E. Andrews 80 Years of Combinatory Analysis
Author: Krishnaswami Alladi
Publisher: Springer Nature
Total Pages: 810
Release: 2021-02-10
Genre: Mathematics
ISBN: 3030570509

This book presents a printed testimony for the fact that George Andrews, one of the world’s leading experts in partitions and q-series for the last several decades, has passed the milestone age of 80. To honor George Andrews on this occasion, the conference “Combinatory Analysis 2018” was organized at the Pennsylvania State University from June 21 to 24, 2018. This volume comprises the original articles from the Special Issue “Combinatory Analysis 2018 – In Honor of George Andrews’ 80th Birthday” resulting from the conference and published in Annals of Combinatorics. In addition to the 37 articles of the Andrews 80 Special Issue, the book includes two new papers. These research contributions explore new grounds and present new achievements, research trends, and problems in the area. The volume is complemented by three special personal contributions: “The Worlds of George Andrews, a daughter’s take” by Amy Alznauer, “My association and collaboration with George Andrews” by Krishna Alladi, and “Ramanujan, his Lost Notebook, its importance” by Bruce Berndt. Another aspect which gives this Andrews volume a truly unique character is the “Photos” collection. In addition to pictures taken at “Combinatory Analysis 2018”, the editors selected a variety of photos, many of them not available elsewhere: “Andrews in Austria”, “Andrews in China”, “Andrews in Florida”, “Andrews in Illinois”, and “Andrews in India”. This volume will be of interest to researchers, PhD students, and interested practitioners working in the area of Combinatory Analysis, q-Series, and related fields.

Advanced Combinatorics

Advanced Combinatorics
Author: Louis Comtet
Publisher: Springer Science & Business Media
Total Pages: 353
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401021961

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Combinatorial Analysis

Combinatorial Analysis
Author: Richard Bellman
Publisher:
Total Pages: 0
Release: 1960
Genre: Combinations
ISBN: 9780821813102

Combinatorial Machine Learning

Combinatorial Machine Learning
Author: Mikhail Moshkov
Publisher: Springer
Total Pages: 186
Release: 2011-06-29
Genre: Technology & Engineering
ISBN: 3642209955

Decision trees and decision rule systems are widely used in different applications as algorithms for problem solving, as predictors, and as a way for knowledge representation. Reducts play key role in the problem of attribute (feature) selection. The aims of this book are (i) the consideration of the sets of decision trees, rules and reducts; (ii) study of relationships among these objects; (iii) design of algorithms for construction of trees, rules and reducts; and (iv) obtaining bounds on their complexity. Applications for supervised machine learning, discrete optimization, analysis of acyclic programs, fault diagnosis, and pattern recognition are considered also. This is a mixture of research monograph and lecture notes. It contains many unpublished results. However, proofs are carefully selected to be understandable for students. The results considered in this book can be useful for researchers in machine learning, data mining and knowledge discovery, especially for those who are working in rough set theory, test theory and logical analysis of data. The book can be used in the creation of courses for graduate students.

Lessons in Play

Lessons in Play
Author: Michael Albert
Publisher: CRC Press
Total Pages: 298
Release: 2007-07-02
Genre: Mathematics
ISBN: 1439864373

Combinatorial games are games of pure strategy involving two players, with perfect information and no element of chance. Starting from the very basics of gameplay and strategy, the authors cover a wide range of topics, from game algebra to special classes of games. Classic techniques are introduced and applied in novel ways to analyze both old and

Combinatory Linguistics

Combinatory Linguistics
Author: Cem Bozsahin
Publisher: Walter de Gruyter
Total Pages: 304
Release: 2012-12-06
Genre: Language Arts & Disciplines
ISBN: 311029687X

The book examines to what extent the mediating relation between constituents and their semantics can arise from combinatory knowledge of words. It traces the roots of Combinatory Categorial Grammar, and uses the theory to promote a Humean question in linguistics and cognitive science: Why do we see limited constituency and dependency in natural languages, despite their diversity and potential infinity? A potential answer is that constituents and dependencies might have arisen from a single resource: adjacency. The combinatory formulation of adjacency constrains possible grammars.