Title

Bounds on Generalized Frobenius Numbers

Document Type

Article

Department

Mathematics (CMC)

Publication Date

4-2011

Abstract

Let N ≥ 2 and let 1 < a1 <⋯< aN be relatively prime integers. The Frobenius number of this N-tuple is defined to be the largest positive integer that has no representation as where x1,…,xN are nonnegative integers. More generally, the s-Frobenius number is defined to be the largest positive integer that has precisely s distinct representations like this. We use techniques from the geometry of numbers to give upper and lower bounds on the s-Frobenius number for any nonnegative integer s.

Comments

This article can also be found at http://arxiv.org/pdf/1008.4937v3.pdf

Rights Information

© 2011 Elsevier Ltd.

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