Herbert S. Wilf

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.

Third Edition

generatingfunctionology

This book is an introductory textbook on the design and analysis of algorithms. The author uses a careful selection of a few topics to illustrate the tools for algorithm analysis. Recursive algorithms are illustrated by Quicksort, FFT, fast matrix multiplications, and others. Algorithms associated with the network flow problem are fundamental in many areas of graph connectivity, matching theory, etc. Algorithms in number theory are discussed with some applications to public key encryption. This second edition will differ from the present edition mainly in that solutions to most of the exercises will be included.

Algorithms and Complexity

Albert Nijenhuis

Combinatorial Algorithms for Computers and Calculators, Second Edition deals with combinatorial algorithms for computers and calculators. Topics covered range from combinatorial families such as the random subset and k-subset of an n-set and Young tableaux, to combinatorial structures including the cycle structure of a permutation and the spanning forest of a graph. Newton forms of a polynomial and the composition of power series are also discussed. Comprised of 30 chapters, this volume begins with an introduction to combinatorial algorithms by considering the generation of all of the 2n subsets of the set {1, 2,...,n}. The discussion then turns to the random subset and k-subset of an n-set; next composition of n into k parts; and random composition of n into k parts. Subsequent chapters focus on sequencing, ranking, and selection algorithms in general combinatorial families; renumbering rows and columns of an array; the cycle structure of a permutation; and the permanent function. Sorting and network flows are also examined, along with the backtrack method and triangular numbering in partially ordered sets. This book will be of value to both students and specialists in the fields of applied mathematics and computer science.

Herbert S. Wilf

About

Books

Join the club