Geodesic
Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 89-91

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

Two results concerning the number $P(2,n)$ of threshold functions and the singularity probability $\mathbb{P}_n$ of random $(n\times n)$ $\{\pm1\}$-matrices are established. The following asymptotics are obtained: $$ P(2,n)\sim2\binom{2^n-1}{n}\text{ and }\mathbb{P}_n\sim n^2\cdot2^{1-n}\quad n\to\infty. $$
Keywords: threshold function, Bernoulli matrices, Möbius function, supermodular function, combinatorial flag. 
@article{DANMA_2020_492_a18,
     author = {A. A. Irmatov},
     title = {Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {89--91},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a18/}
}
TY  - JOUR
AU  - A. A. Irmatov
TI  - Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 89
EP  - 91
VL  - 492
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_492_a18/
LA  - ru
ID  - DANMA_2020_492_a18
ER  - 
%0 Journal Article
%A A. A. Irmatov
%T Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 89-91
%V 492
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_492_a18/
%G ru
%F DANMA_2020_492_a18
A. A. Irmatov. Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 89-91. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a18/