An optimal lower bound for the Frobenius problem

By I. Aliev, Peter M. Gruber. 2005

49 citations recorded by the source corpus.

Abstract Given N ⩾ 2 positive integers a 1 , a 2 , … , a N with GCD ( a 1 , … , a N ) = 1 , let f N denote the largest natural number which is not a positive integer combination of a 1 , … , a N . This paper gives an optimal lower bound for f N in terms of the absolute inhomogeneous minimum of the standard ( N − 1 ) -simplex.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/657dc87d701b4bf402c688f6ddc155894fa8d909

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Igor E. Shparlinski
2. Jens Marklof
3. Andreas Strombergsson

In Computational Theory and Mathematics

1. Igor E. Shparlinski
2. Jens Marklof

In Geometry and Topology

1. Igor E. Shparlinski
2. Jens Marklof
3. Richard A. Brualdi
4. Berk Ustun
5. Cynthia Rudin

Citations in the corpus

• Modular hyperbolas (2011, result): “Several other recent results can be found in [3, 4, 38, 89, 187].”
• The asymptotic distribution of Frobenius numbers (2009, background): “It is proved in [1] that ρ∗ > ((d− 1)!)1/(d−1) > 0, and so in particular (1.”