Exponential Lower Bounds for the Numbers of Skolem-Type Sequences

Abstract

It was shown by Abrham that the number of pure Skolem sequences of order $n$, $n\equiv 0$ or $1(\mathrm{mod}4)$, and the number of extended Skolem sequences of order $n$, are both bounded below by $2^{\lfloor \frac{n}{3}\rfloor }$. These results are extended to give similar lower bounds for the numbers of hooked Skolem sequences, split Skolem sequences, and split-hooked Skolem sequences.