Geodesic
Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 822-828 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we obtain an asymptotic approximation of the number $K_n$ of repetition-free Boolean functions of $n$ variables in the elementary basis $\{\&,\vee,-\}$ as $n\to\infty$ with relative error $O(1/\sqrt n\,)$. As a consequence, we verify conjectures on the existence of constants $\delta$ and $\alpha$ such that $$ K_n\sim\delta\cdot\alpha^{n-1}\cdot(2n-3)!!, $$ and obtain these constants.
Keywords: repetition-free Boolean function, Euler number, Stirling number of the second kind, improper integral, two-pole serial set. 
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O. V. Zubkov. Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis. Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 822-828. http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/

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