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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 492, Pages 89–91
DOI: https://doi.org/10.31857/S2686954320030091 (Mi danma79) 		 
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
Full-text PDF (161 kB) Citations (3)
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DOI: https://doi.org/10.31857/S2686954320030091
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.
Funding agency Grant number
Russian Foundation for Basic Research 18–01–00398 A
This work was supported in part by the Russian Foundation for Basic Research, grant no. 18-01-00398 A.
Presented: A. T. Fomenko
Received: 04.03.2020
Revised: 04.03.2020
Accepted: 19.03.2020
English version:
Doklady Mathematics, 2020, Volume 101, Issue 3, Pages 247–249
DOI: https://doi.org/10.1134/S1064562420030096
Bibliographic databases:
Document Type: Article
UDC: 519.1, 519.7
Language: Russian
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
Citation in format AMSBIB
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\by A.~A.~Irmatov
\paper Asymptotics of the number of threshold functions and the singularity probability of random $\{\pm1\}$-matrices
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\vol 492
\pages 89--91
\mathnet{http://mi.mathnet.ru/danma79}
\crossref{https://doi.org/10.31857/S2686954320030091}
\zmath{https://zbmath.org/?q=an:1474.60012}
\elib{https://elibrary.ru/item.asp?id=42930029}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 3
\pages 247--249
\crossref{https://doi.org/10.1134/S1064562420030096}
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    • This publication is cited in the following 3 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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