The Diophantine Frobenius Problem

Erscheinungsjahr 2005
ISBN: 978-0-19-856820-9
Verlag: OUP Oxford

Buch, Englisch, 260 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 558 g

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.

Zielgruppe

Graduates and researchers in pure mathematics, particularly number theory

Autoren/Hrsg.

Ramírez Alfonsín, Jorge L.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Populärwissenschaftliche Werke

Inhaltsverzeichnis

- 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

Über Autor(innen)

Jorge L. Ramírez Alfonsín, Maître de Conférences, Université Pierre et Marie Curie, Paris 6