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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{MZM_2010_87_5_a6,
     author = {O. V. Zubkov},
     title = {Refined {Estimates} of the {Number} of {Repetition-Free} {Boolean} {Functions} in the {Full} {Binary} {Basis} $\{\&,\vee,\oplus,-\}$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {721--733},
     publisher = {mathdoc},
     volume = {87},
     number = {5},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a6/}
}
TY  - JOUR
AU  - O. V. Zubkov
TI  - Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{\&,\vee,\oplus,-\}$
JO  - Matematičeskie zametki
PY  - 2010
SP  - 721
EP  - 733
VL  - 87
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a6/
LA  - ru
ID  - MZM_2010_87_5_a6
ER  - 
%0 Journal Article
%A O. V. Zubkov
%T Refined Estimates of the Number of Repetition-Free Boolean Functions in the Full Binary Basis $\{\&,\vee,\oplus,-\}$
%J Matematičeskie zametki
%D 2010
%P 721-733
%V 87
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_87_5_a6/
%G ru
%F MZM_2010_87_5_a6
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/