Geodesic
On irreducible algebraic sets over linearly ordered semilattices~II
Prikladnaâ diskretnaâ matematika, no. 4 (2017), pp. 49-56.

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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. 
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A. N. Shevlyakov. On irreducible algebraic sets over linearly ordered semilattices~II. Prikladnaâ diskretnaâ matematika, no. 4 (2017), pp. 49-56. http://geodesic.mathdoc.fr/item/PDM_2017_4_a2/

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