On the distance between Frobenius numbers

Aliev, Iskander ORCID: https://orcid.org/0000-0002-2206-9207 and Mohammed, Dilbak 2015. On the distance between Frobenius numbers. Moscow Journal of Combinatorics and Number Theory 5 (4) , pp. 205-214.

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Abstract

Let n ≥ 2 and k ≥ 1 be integers and a = (a_1,...,a_n) be an integer vector with positive coprime entries. The k-Frobenius number F_k(a) is the largest integer that cannot be represented as a nonnegative integer combination of a_i in at least k different ways. We study the quantity (F_k(a) − F_1(a))(a1···an)^(−1/(n−1)) and use obtained results to improve existing upper bounds for 2-Frobenius numbers. The proofs are based on packing and covering results from the geometry of numbers.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Moscow Institute of Physics and Technology
ISSN:	2220-5438
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	9 October 2015
Last Modified:	22 Nov 2024 07:15
URI:	https://orca.cardiff.ac.uk/id/eprint/87667

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