Geodesic
Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis
Matematičeskie zametki, Tome 82 (2007) no. 6, pp. 822-828.

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

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. 
@article{MZM_2007_82_6_a2,
     author = {O. V. Zubkov},
     title = {Asymptotics of the {Number} of {Repetition-Free} {Boolean} {Functions} in the {Elementary} {Basis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {822--828},
     publisher = {mathdoc},
     volume = {82},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/}
}
TY  - JOUR
AU  - O. V. Zubkov
TI  - Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis
JO  - Matematičeskie zametki
PY  - 2007
SP  - 822
EP  - 828
VL  - 82
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/
LA  - ru
ID  - MZM_2007_82_6_a2
ER  - 
%0 Journal Article
%A O. V. Zubkov
%T Asymptotics of the Number of Repetition-Free Boolean Functions in the Elementary Basis
%J Matematičeskie zametki
%D 2007
%P 822-828
%V 82
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_82_6_a2/
%G ru
%F MZM_2007_82_6_a2
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/

[1] A. C. Balyuk, S. F. Vinokurov, A. I. Gaidukov, O. V. Zubkov, K. D. Kirichenko, V. I. Panteleev, N. A. Peryazev, Yu. V. Peryazeva, Izbrannye voprosy teorii bulevykh funktsii, eds. S. F. Vinokurov, N. A. Peryazev, Fizmatlit, M., 2001 | Zbl

[2] O. B. Zubkov, “Nakhozhdenie chisla bespovtornykh bulevykh funktsii v elementarnom bazise v vide skhodyaschegosya ryada”, Trudy VII Mezhdunarodnoi konferentsii “Diskretnye modeli v teorii upravlyayuschikh sistem”, Izd-vo Maks Press, M., 2006, 125–129

[3] O. B. Zubkov, Otsenki chisla bespovtornykh bulevykh funktsii v binarnykh bazisakh, Diskretnaya matematika i informatika, 15, Izd-vo Irkutskogo un-ta, Irkutsk, 2002

[4] O. B. Zubkov, “Nakhozhdenie chisla bespovtornykh bulevykh funktsii v elementarnom bazise pri pomoschi chisel Stirlinga vtorogo roda”, Vestn. Buryatskogo un-ta. Ser. 13. Matem., inform., 2, Izd-vo Buryatskogo un-ta, Ulan-Ude, 2005, 12–16

[5] H. A. Peryazev, “Predstavlenie funktsii algebry logiki bespovtornymi formulami”, Tezisy soobschenii XI Mezhrespublikanskoi konferentsii po matematicheskoi logike, KazGU, Kazan, 1992, 110

[6] Dzh. Riordan, Vvedenie v kombinatornyi analiz, IL, M., 1963 | MR | Zbl

[7] A. P. Prudnikov, Yu. A. Brychkov, O. I. Marichev, Integraly i ryady: Elementarnye funktsii, Nauka, M., 1981 | MR | Zbl