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The Diophantine Frobenius problem. (English) Zbl 1134.11012
Oxford Lecture Series in Mathematics and its Applications 30. Oxford: Oxford University Press (ISBN 0-19-856820-7/hbk). xvi, 243 p. (2005).
This book gives a comprehensive survey of what is known today on the Frobenius problem. Both the Frobenius number and the Sylvester denumerant, i.e. the number of solutions of \(m= \sum^n_{i=1} a_i x_i\) with integers \(x_i\geq 0\) are considered. Computational aspects as well as theoretical results and applications are discussed, and beside the general problem also special cases are taken into consideration. At the end of each chapter some supplementary notes referring further results are given. Two appendices contain problems and conjectures resp. some theoretical aspects used in the text. The bibliography with 492 items shows the carefulness of the presentation.

MSC:
11D04 Linear Diophantine equations
11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11P81 Elementary theory of partitions
05A17 Combinatorial aspects of partitions of integers
11Y50 Computer solution of Diophantine equations
20M14 Commutative semigroups
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