Geodesic
On the number of additive permutations and Skolem-type sequences
Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 415-432.

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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⌋.
DOI : 10.26493/1855-3974.1098.ca0
Keywords: Additive permutation, Skolem sequence, transversal 
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Diane M. Donovan; Michael J. Grannell. On the number of additive permutations and Skolem-type sequences. Ars Mathematica Contemporanea, Tome 14 (2018) no. 2, pp. 415-432. doi : 10.26493/1855-3974.1098.ca0. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1098.ca0/

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