Pub. Date:
Oxford University Press, USA
The Diophantine Frobenius Problem

The Diophantine Frobenius Problem

by J. L. Ramirez Alfonsin


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During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised the 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 FB 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.

Product Details

ISBN-13: 9780198568209
Publisher: Oxford University Press, USA
Publication date: 02/02/2006
Series: Oxford Lecture Series in Mathematics and Its Applications Series , #30
Pages: 260
Sales rank: 1,032,520
Product dimensions: 9.30(w) x 6.30(h) x 0.80(d)

About the Author

Universite Pierre et Marie Curie, Paris

Table of Contents

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

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