Geodesic
Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{\,\vee,\oplus,-\}$
Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 721-733 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider repetition-free Boolean functions in the basis $\{\&,\vee,\oplus,-\}$, and prove a formula expressing the number of such functions of $n$ variables as a product of Fibonacci numbers. These products are estimated; as a result, we obtain asymptotic estimates for the number of repetition-free Boolean functions. These estimates involve Euler numbers of second order and can be reduced by well-known methods to the form of an exponential-power series. These estimates can be used to construct the final asymptotics of the number of repetition-free Boolean functions in the full binary basis.
Keywords: repetition-free Boolean function, full binary basis, binary function, Fibonacci numbers, Euler numbers, index preserving structure. 
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O. V. Zubkov. Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{\&,\vee,\oplus,-\}$. Matematičeskie zametki, Tome 87 (2010) no. 5, pp. 721-733. http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a6/

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