Expected Frobenius numbers

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207, Henk, Martin and Hinrichs, Aicke 2011. Expected Frobenius numbers. Journal of Combinatorial Theory, Series A 118 (2) , pp. 525-531. 10.1016/j.jcta.2009.12.012

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Frobenius number; Geometry of numbers; Reverse AGM inequality; Knapsack polytope
Publisher:	Elsevier
ISSN:	0097-3165
Last Modified:	13 Jan 2023 02:14
URI:	https://orca.cardiff.ac.uk/id/eprint/24982

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