The diophantine frobenius problem
著者
書誌事項
The diophantine frobenius problem
（Oxford lecture series in mathematics and its applications, 30）
Oxford University Press, 2005
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, .
At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
目次
- Preface
- Acknowledgements
- 1. Algorithmic Aspects
- 2. The Frobenius Number for Small n
- 3. The General Problem
- 4. Sylvester Denumerant
- 5. Integers without Representation
- 6. Generalizations and Related Problems
- 7. Numerical Semigroups
- 8. Applications of the Frobenius Number
- 9. Appendix A
- Bibliography
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