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⌋.
@article{1098,
title = {On the number of additive permutations and Skolem-type sequences},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {14},
year = {2017},
doi = {10.26493/1855-3974.1098.ca0},
language = {EN},
url = {http://dml.mathdoc.fr/item/1098}
}
Donovan, Diane M.; Grannell, Michael J. On the number of additive permutations and Skolem-type sequences. ARS MATHEMATICA CONTEMPORANEA, Tome 14 (2017) . doi : 10.26493/1855-3974.1098.ca0. http://gdmltest.u-ga.fr/item/1098/