Geodesic
On the number of threshold functions
Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 40-43
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A Boolean function is called a threshold function if its truth domain is a part of the $n$-cube cut off by some hyperplane. The number of threshold functions of $n$ variables $P(2,n)$ was estimated in [1, 2, 3]. Obtaining the lower bounds is a problem of special difficulty. Using a result of [4], Yu. A. Zuev showed [3] that for sufficiently large $n$ $$ P(2,n)>2^{n^2(1-10/\ln n)}. $$ In the present paper a new proof which gives a more precise lower bound of $P(2,n)$ is proposed, namely, it is proved that for sufficiently large $n$ $$ P(2,n)>2^{n^2(1-7/\ln n)}P\biggl(2,\biggl[\frac{7(n-1)\ln 2}{\ln(n-1)}\biggr]\biggr). $$ 
@article{DM_1993_5_3_a2,
     author = {A. A. Irmatov},
     title = {On the number of threshold functions},
     journal = {Diskretnaya Matematika},
     pages = {40--43},
     year = {1993},
     volume = {5},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1993_5_3_a2/}
}
TY  - JOUR
AU  - A. A. Irmatov
TI  - On the number of threshold functions
JO  - Diskretnaya Matematika
PY  - 1993
SP  - 40
EP  - 43
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DM_1993_5_3_a2/
LA  - ru
ID  - DM_1993_5_3_a2
ER  - 
%0 Journal Article
%A A. A. Irmatov
%T On the number of threshold functions
%J Diskretnaya Matematika
%D 1993
%P 40-43
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/DM_1993_5_3_a2/
%G ru
%F DM_1993_5_3_a2
A. A. Irmatov. On the number of threshold functions. Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 40-43. http://geodesic.mathdoc.fr/item/DM_1993_5_3_a2/