Expected Frobenius numbers

Authors:
Iskander Aliev;Martin Henk;Aicke Hinrichs
Affiliations:
School of Mathematics and Wales Institute of Mathematical and Computational Sciences, Cardiff University, Senghennydd Road, Cardiff, Wales, UK;Institut für Algebra und Geometrie, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, D-39106-Magdeburg, Germany;Friedrich Schiller Universität Jena, Fakultät für Mathematik und Informatik, Ernst-Abbe-Platz 2, D-07743 Jena, Germany
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 6
Cited 1

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Solving thousand-digit Frobenius problems using Gröbner bases

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On test sets for nonlinear integer maximization

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Feasibility of Integer Knapsacks

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Abstract

Given a primitive positive integer vector a, the Frobenius number F(a) is the largest integer that cannot be represented as a non-negative integral combination of the coordinates of a. We show that for large instances the order of magnitude of the expected Frobenius number is (up to a constant depending only on the dimension) given by its lower bound.