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.
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)
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 |