Schott, René; Staples, G. Stacey 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. Reviewer: Benoît Collins (Ottawa) Cited in 12 Documents 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 Keywords:Clifford algebras; operator calculus; graph theory; quantum probability; geometric graph processes; time-homogeneous random walks; dynamic walks; iterated stochastic integrals; partition-dependent stochastic measures; Appell systems; operator (co)homology Software:GluCat; CliffSymNil; CliffOC; CliffMath; Gaigen; Mathematica PDFBibTeX XMLCite \textit{R. Schott} and \textit{G. S. Staples}, Operator calculus on graphs. Theory and applications in computer science. London: Imperial College Press (2012; Zbl 1264.15025) Full Text: Link