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The aim of this paper is to construct interpolation functions for the numbers of the k-ary Lyndon words which count n digit primitive necklace class representative on the set of the k-letter alphabet. By using the unified zeta-type function and the unification of the Apostol-type numbers which are defined by Ozden et al. (Comput Math Appl 60:2779–2787, 2010), we give an alternating series for the...
The main motivation of this paper was to give finite and infinite generating functions for the numbers of the k-ary Lyndon words and necklaces. In order to construct our new generating functions, we use two different methods. The first method is related to the derivative operator $$t\frac{d}{\mathrm{d}t}$$ t d d t and the Stirling numbers of the second kind. On the other hand, the second...
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