Generalized Frobenius Numbers: Bounds and Average Behavior

Authors

Iskander Aliev
Lenny Fukshansky, Claremont McKenna CollegeFollow
Martin Henk

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2012

Abstract

The proof of Theorem 1.1 is based on a generalization of a result of Kannan which relates the classical Frobenius number to the covering radius of a certain simplex with respect to a certain lattice. In our setting we need a kind of generalized covering radius, whose definition as well as some properties and background information from the Geometry of Numbers will be given in Section 2. In Section 3 we will prove, analogously to the mentioned result of Kannan, an identity between F_s(a) and this generalized covering radius and will present a proof of Theorem 1.1. The last section contains a proof of Corollary 1.2.

Rights Information

© 2012 IMPAN

Recommended Citation

Aliev, Iskander, Lenny Fukshansky, and Martin Henk. "Generalized Frobenius Numbers: Bounds and Average Behavior." Acta Arithmetica 155.1 (2012): 53-62.