The Diophantine Frobenius Problem

Hardcover | December 29, 2005

byJorge L. Ramirez Alfonsin

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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 ia1,...,an,/i find the largest natural number (called the Frobenius number and denoted by ig(a1,...,an/i)that is not representable as a nonnegative integer combination of ia1,...,an,/i .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 formulagiving 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.

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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 ia1,...,an,/i find the largest natural number (called the Frobenius number and denoted by ig(a1,...,an/i)that is not representable as a nonnegative i...

Jorge L. Ramirez Alfonsin is at Maitre de Conferences, Universite Pierre et Marie Curie, Paris 6.
Format:HardcoverDimensions:264 pages, 9.21 × 6.14 × 0.78 inPublished:December 29, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198568207

ISBN - 13:9780198568209

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Table of Contents

PrefaceAcknowledgements1. Algorithmic Aspects2. The Frobenius Number for Small n3. The General Problem4. Sylvester Denumerant5. Integers without Representation6. Generalizations and Related Problems7. Numerical Semigroups8. Applications of the Frobenius Number9. Appendix ABibliography