On the number of additive permutations and Skolem-type sequences

Diane M. Donovan, Michael J. Grannell

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⌋.

Keywords


Additive permutation, Skolem sequence, transversal

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ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications