This book focuses on symmetric groups and representation theory. The symmetric group is a central object in discrete mathematics. It can be studied from a combinatorial, algorithmic, or algebraic viewpoint, and the results can be applied in a plethora of other fields, such as physics and computer science. This book is the most up-to-date one on the topic, bringing together new research and results.

Get an In-Depth Understanding of Graph Drawing Techniques, Algorithms, Software, and Applications

The Handbook of Graph Drawing and Visualization provides a broad, up-to-date survey of the field of graph drawing. It covers topological and geometric foundations, algorithms, software systems, and visualization applications in business, education, science, and engineering. Each chapter is self-contained and includes extensive references.

The first several chapters of the book deal with fundamental topological and geometric concepts and...

Applicable to any problem that requires a finite number of solutions, finite state-based models (also called finite state machines or finite state automata) have found wide use in various areas of computer science and engineering. Handbook of Finite State Based Models and Applications provides a complete collection of introductory materials on finite state theories, algorithms, and the latest domain applications. For beginners, the book is a handy reference for quickly looking up model details. For more experienced researchers, it is suitable as a source of in-depth study...

Finite configurations of geometric primitives under local metric and algebraic constraints arise in many situations in mathematics as well as in engineering and science applications. The former situations result in multiple perspectives, tools and techniques from algebraic geometry and topology; from combinatorics; from finite metric spaces, asymptotic geometry and convex analysis; and from complexity. The latter situations give rise to fresh new problems and directions.

Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics.

Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules,...