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This article is cited in 3 scientific papers (total in 3 papers)
INFORMATICS
Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices
A. A. Irmatov Lomonosov Moscow State University, Moscow, Russian Federation
Abstract:
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.
Citation:
A. A. Irmatov, “Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices”, Dokl. RAN. Math. Inf. Proc. Upr., 492 (2020), 89–91; Dokl. Math., 101:3 (2020), 247–249
Linking options:
https://www.mathnet.ru/eng/danma79 https://www.mathnet.ru/eng/danma/v492/p89
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