Bounds on Generalized Frobenius Numbers

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow
Achill Schürmann, University of Rostock

Document Type

Article

Department

Mathematics (CMC)

Publication Date

4-2011

Abstract

Let N ≥ 2 and let 1 < a₁ <⋯< a_N 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,…,x_N 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.

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

http://dx.doi.org/10.1016/j.ejc.2010.11.001

Recommended Citation

Fukshansky, Lenny, and Achill Schürmann. "Bounds on Generalized Frobenius Numbers." European Journal of Combinatorics 32.3 (2011): 361-368. Web.