Combinatorial Enumeration
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Combinatorial Enumeration
Author: Ian P. Goulden
language: en
Publisher: Courier Corporation
Release Date: 2004-06-23
This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.
Symmetry and Combinatorial Enumeration in Chemistry
Author: Shinsaku Fujita
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is written to introduce a new approach to stereochemical problems and to combinatorial enumerations in chemistry. This approach is based on group the ory, but different from conventional ways adopted by most textbooks on chemical group theory. The difference sterns from their starting points: conjugate subgroups and conjugacy classes. The conventional textbooks deal with linear representations and character ta bles of point groups. This fact implies that they lay stress on conjugacy classesj in fact, such group characters are determined for the respective conjugacy classes. This approach is versatile, since conjugacy classes can be easily obtained by ex amining every element of a group. It is unnecessary to know the group-subgroup relationship of the group, which is not always easy to obtain. The same situa tion is true for chemical enumerations, though these are founded on permutation groups. Thus, the P6lya-Redfield theorem (1935 and 1927) uses a cycle index that is composed of terms associated with conjugacy classes.
Combinatorial Algorithms
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.