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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
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.
Citation:
A. N. Shevlyakov, “On irreducible algebraic sets over linearly ordered semilattices II”, Prikl. Diskr. Mat., 2017, no. 38, 49–56
Linking options:
https://www.mathnet.ru/eng/pdm605 https://www.mathnet.ru/eng/pdm/y2017/i4/p49
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Abstract page: | 143 | Full-text PDF : | 50 | References: | 42 |
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