On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\,\lor,\oplus,\lnot\}$
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 158-159.

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

We obtain an asymptotic formula for the number $S_n$ of repetition-free Boolean functions of $n$ variables in the basis $\{\,\lor,\oplus,\lnot\}$ for $n\to\infty: S_n\sim cn^{-3/2}\alpha^nn!$, where $c\approx0.1998398363\;,\alpha\approx7.549773429\;.$
Keywords: repetition-free Boolean function, enumeration, asymptotics.
@article{DM_2015_27_3_a10,
     author = {V. A. Voblyi},
     title = {On the asymptotics of the number of repetition-free {Boolean} functions in the basis $\{\&,\lor,\oplus,\lnot\}$},
     journal = {Diskretnaya Matematika},
     pages = {158--159},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/}
}
TY  - JOUR
AU  - V. A. Voblyi
TI  - On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$
JO  - Diskretnaya Matematika
PY  - 2015
SP  - 158
EP  - 159
VL  - 27
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/
LA  - ru
ID  - DM_2015_27_3_a10
ER  - 
%0 Journal Article
%A V. A. Voblyi
%T On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$
%J Diskretnaya Matematika
%D 2015
%P 158-159
%V 27
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/
%G ru
%F DM_2015_27_3_a10
V. A. Voblyi. On the asymptotics of the number of repetition-free Boolean functions in the basis $\{\&,\lor,\oplus,\lnot\}$. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 158-159. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a10/

[1] Izbrannye voprosy teorii bulevykh funktsii, Pod red. S.F. Vinokurova i N.A. Peryazeva, Fizmatlit, Moskva, 2001, 192 pp.

[2] Zubkov O.V., “Uluchshennye otsenki chisla bespovtornykh bulevykh funktsii v polnom binarnom bazise $\{\,\lor,\oplus,\lnot\}$”, Matem. zametki, 87:5 (2010), 721–733 | DOI | MR | Zbl

[3] Voblyi V.A., “Asimptotika chisla bespovtornykh bulevykh funktsii v bazise $B_1$”, Diskretnaya matematika, 22:4 (2010), 156–157 | DOI | MR | Zbl

[4] Lavrentev M.A., Shabat B.M., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1965, 716 pp. | MR