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Operator calculus on graphs. Theory and applications in computer science. (English) Zbl 1264.15025

London: Imperial College Press (ISBN 978-1-84816-876-3/hbk; 978-1-84816-877-0/ebook). xv, 411 p. (2012).
This book focuses on the study of Clifford algebras and their applications to operator calculus, graph theory and quantum probability theory. An emphasis is put on the combinatorial and graph theoretic aspects of Clifford algebras. Many Mathematica examples are presented throughout the book. It is intended for an audience of mathematicians, physicists, and computer scientists.
After a first part with a theoretical introduction to combinatorial algebras and their properties, the authors present applications to combinatorics and graph theory, probability on algebraic structures, operator calculus, and symbolic computations.

MSC:

15A66 Clifford algebras, spinors
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
33C65 Appell, Horn and Lauricella functions
05C81 Random walks on graphs
05C90 Applications of graph theory
81P45 Quantum information, communication, networks (quantum-theoretic aspects)
15-02 Research exposition (monographs, survey articles) pertaining to linear algebra
44A45 Classical operational calculus
68W30 Symbolic computation and algebraic computation
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
60G50 Sums of independent random variables; random walks
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