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基本説明
The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.
Full Description
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.
Contents
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
