Clifford Algebras and Zeons

Clifford algebras have many well-known applications in physics, engineering, and computer graphics. Zeon algebras are subalgebras of Clifford algebras whose combinatorial properties lend them to graph-theoretic applications such as enumerating minimal cost paths in dynamic networks. This book provides a foundational working knowledge of zeon algebras, their properties, and their potential applications in an increasingly technological world.

As a graduate-level or advanced undergraduate-level mathematics textbook, it is suitable for self-study by researchers interested in new approaches to existing combinatorial problems and applications (wireless networks, Boolean satisfiability, coding theory, etc.).

As the first textbook to explore algebraic and combinatorial properties of zeon algebras in depth, it is suitable for interdisciplinary study in analysis, algebra, and combinatorics. The material is complemented by the CliffMath software package for Mathematica, which is freely available through the book's webpage.
Contents: The Essentials:AlgebraCombinatoricsGeometric Algebra:Geometry of the Complex PlaneQuaternionsEuclidean Clifford AlgebrasClifford Algebras of Arbitrary SignatureDecompositions in COQ(V)From Geometry to CombinatoricsAlgebraic Combinatorics & Zeons:Algebraic and Combinatorial Properties of ZeonsZeon PolynomialsNorms and Inequalities in Zeon AlgebrasZeon MatricesZeon Functions and FactorizationsZeon Differential CalculusGraph Enumeration ProblemsGraph Colorings and Chromatic StructuresBoolean SatisfiabilityInduced Operators:Induced Operators and Kravchuk PolynomialsGraph-Induced OperatorsSolutions and Hints to Selected Exercises
Readership: Advanced undergraduate students, graduate students and researchers in the field of combinatorics and its applications.Clifford Algebras;Zeons;Combinatorics0Key Features:While there are a number of books focusing on Clifford algebras, the only other title related to zeon algebras is the author's research monograph, Operator Calculus on GraphsWhere the previous book focused on a wide array of topics and applications, this book is constructed as a textbook, with exercises and solutions. It includes an introduction to Clifford (geometric) algebras, before constructing zeon algebras as Clifford subalgebrasThe bulk of the material on algebraic and combinatorial aspects of zeons in Part III is new, as is the "higher-level" material in Part IV. The material is organized in a careful progression from geometry to combinatorics (and beyond)The material should be of interest not only to students of mathematics, but to mathematicians, computer scientists, and engineers looking for new approaches to existing combinatorial problems (wireless networks, Boolean satisfiability, coding theory, etc.)