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