Geodesic
Finding and estimating the number of repetition-free Boolean functions over the elementary basis in the form of a convergent series
Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 30-38
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We obtain a representation of the number $K_n$ of repetition-free Boolean functions of $n$ variables over the elementary basis $\{\,\vee,\bar{}\,\}$ in the form of a convergent exponential power series. This representation is the simplest representation among a number of similar formulas containing different combinatorial numbers. The obtained result gives a possibility to find the asymptotics of $K_n$. 
@article{DM_2009_21_4_a2,
     author = {O. V. Zubkov},
     title = {Finding and estimating the number of repetition-free {Boolean} functions over the elementary basis in the form of a~convergent series},
     journal = {Diskretnaya Matematika},
     pages = {30--38},
     year = {2009},
     volume = {21},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2009_21_4_a2/}
}
TY  - JOUR
AU  - O. V. Zubkov
TI  - Finding and estimating the number of repetition-free Boolean functions over the elementary basis in the form of a convergent series
JO  - Diskretnaya Matematika
PY  - 2009
SP  - 30
EP  - 38
VL  - 21
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_2009_21_4_a2/
LA  - ru
ID  - DM_2009_21_4_a2
ER  - 
%0 Journal Article
%A O. V. Zubkov
%T Finding and estimating the number of repetition-free Boolean functions over the elementary basis in the form of a convergent series
%J Diskretnaya Matematika
%D 2009
%P 30-38
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/DM_2009_21_4_a2/
%G ru
%F DM_2009_21_4_a2
O. V. Zubkov. Finding and estimating the number of repetition-free Boolean functions over the elementary basis in the form of a convergent series. Diskretnaya Matematika, Tome 21 (2009) no. 4, pp. 30-38. http://geodesic.mathdoc.fr/item/DM_2009_21_4_a2/

[1] Vinokurov S. F., Peryazev N. A., Izbrannye voprosy teorii bulevykh funktsii, Fizmatlit, Moskva, 2001 | Zbl

[2] Grekhem R., Knut D., Patashnik O., Konkretnaya matematika. Osnovanie informatiki, Mir, Moskva, 1998

[3] Zubkov O. V., “Nakhozhdenie chisla bespovtornykh bulevykh funktsii v elementarnom bazise pri pomoschi chisel Stirlinga vtorogo roda”, Vestnik Buryatskogo universiteta, seriya 13: matematika i informatika, 2005, no. 2, 12–16 | MR

[4] Zubkov O. V., “Asimptotika chisla bespovtornykh bulevykh funktsii v elementarnom bazise”, Matem. zametki, 82:6 (2007), 822–828 | MR | Zbl

[5] Peryazev N. A., “Predstavlenie funktsii algebry logiki bespovtornymi formulami”, Tezisy KhI Mezhrespubl. konf. po matematicheskoi logike, Kazan, 1992, 110

[6] Riordan Dzh., Vvedenie v kombinatornyi analiz, IL, Moskva, 1963