The Diophantine Frobenius Problem

Jorge L. Ramirez Alfonsin - Collection Oxford Lecture Series in Mathematics and Its Applications

260 pages, parution le 15/01/2006

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Résumé

First text to summarise the results of the Frobenius problem
All main theorems treated
Methods thoroughly illustrated with examples

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.

Readership: Graduates and researchers in pure mathematics, particularly number theory

L'auteur - Jorge L. Ramirez Alfonsin

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

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Sommaire

Algorithmic Aspects
The Frobenius Number for Small n
The General Problem
Sylvester Denumerant
Integers without Representation
Generalizations and Related Problems
Numerical Semigroups
Applications of the Frobenius Number
Appendix A : problems and conjectures

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Oxford University Press
Auteur(s)	Jorge L. Ramirez Alfonsin
Collection	Oxford Lecture Series in Mathematics and Its Applications
Parution	15/01/2006
Nb. de pages	260
Format	16 x 24
Couverture	Relié
Poids	520g
Intérieur	Noir et Blanc
EAN13	9780198568209
ISBN13	978-0-19-856820-9