An optimal lower bound for the Frobenius problem |
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| Authors: | Iskander M. Aliev Peter M. Gruber |
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| Affiliation: | a School of Mathematics, University of Edinburgh, King's Buildings, Edinburgh EH9 3JZ, UK
b Technische Universität Wien, Wiedner Hauptstraße 8-10/1046, 1040 Wien, Austria |
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| Abstract: | Given N?2 positive integers a1,a2,…,aN with GCD(a1,…,aN)=1, let fN denote the largest natural number which is not a positive integer combination of a1,…,aN. This paper gives an optimal lower bound for fN in terms of the absolute inhomogeneous minimum of the standard (N−1)-simplex. |
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| Keywords: | 11D85 11H31 52C17 |
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