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Prikladnaya Diskretnaya Matematika, 2017, Number 38, Pages 49–56
DOI: https://doi.org/10.17223/20710410/38/3
(Mi pdm605)
 

Theoretical Backgrounds of Applied Discrete Mathematics

On irreducible algebraic sets over linearly ordered semilattices II

A. N. Shevlyakovab

a Sobolev Institute of Mathematics, Omsk, Russia
b Omsk State Technical University, Omsk, Russia
References:
Abstract: Equations over finite linearly ordered semilattices are studied. It is assumed that the order of a semilattice is not less than the number of variables in an equation. For any equation $t(X)=s(X)$, we find irreducible components of its solution set. We also compute the average number $\overline{\mathrm{Irr}}(n)$ of irreducible components for all equations in $n$ variables. It turns out that $\overline{\mathrm{Irr}}(n)$ and the function $\frac49n!$ are asymptotically equivalent.
Keywords: irreducible components, algebraic sets, semilattices.
Funding agency Grant number
Russian Science Foundation 17-11-01117
The author was supported by the RSF-grant 17-11-01117.
Bibliographic databases:
Document Type: Article
UDC: 512.53
Language: English
Citation: A. N. Shevlyakov, “On irreducible algebraic sets over linearly ordered semilattices II”, Prikl. Diskr. Mat., 2017, no. 38, 49–56
Citation in format AMSBIB
\Bibitem{She17}
\by A.~N.~Shevlyakov
\paper On irreducible algebraic sets over linearly ordered semilattices~II
\jour Prikl. Diskr. Mat.
\yr 2017
\issue 38
\pages 49--56
\mathnet{http://mi.mathnet.ru/pdm605}
\crossref{https://doi.org/10.17223/20710410/38/3}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000422797800003}
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    Прикладная дискретная математика
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