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