On the number of additive permutations and Skolem-type sequences

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). We adapt their proof to show that for sufficiently large t the number of additive permutations on [−t, t] is greater than (3.246) 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). This compares with the previous best bound of 2. AMS classifications: 05B07, 05B10.