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On the number of additive permutations and Skolem-type sequences

Donovan, Diane and Grannell, Mike (2018). On the number of additive permutations and Skolem-type sequences. Ars Mathematica Contemporanea, 14 pp. 415–432.

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Abstract

Cavenagh and Wanless recently proved that, for sufficiently large odd n, the number of transversals in the Latin square formed from the addition table for integers modulo n is greater than (3.246)n. We adapt their proof to show that for sufficiently large t the number of additive permutations on [-t,t] is greater than (3.246)2t+1 and we go on to derive some much improved lower bounds on the numbers of Skolem-type sequences. For example, it is shown that for sufficiently large t ≡ 0$ or 3 (mod 4), the number of split Skolem sequences of order n=7t+3 is greater than (3.246)6t+3. This compares with the previous best bound of 2n/3⌋.

Item Type: Journal Item
Copyright Holders: 2017 Journal
ISSN: 1855-3974
Extra Information: AMS classifications: 05B07, 05B10.
Keywords: Additive permutation; Skolem sequence; Transversal.
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 49513
Depositing User: Mike Grannell
Date Deposited: 10 Nov 2017 14:13
Last Modified: 11 Jan 2018 16:36
URI: http://oro.open.ac.uk/id/eprint/49513
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