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.

URL: http://amc-journal.eu/index.php/amc/article/view/1...

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 2^⌊n/3⌋.

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About

• Item ORO ID
• 49513
• Item Type
• Journal Item
• ISSN
• 1855-3974
• Extra Information
• AMS classifications: 05B07, 05B10.
• Keywords
• Additive permutation; Skolem sequence; Transversal.
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2017 Journal
• Depositing User
• Mike Grannell