Geodesic
Random equations over free semilattices
Prikladnaâ diskretnaâ matematika, no. 2 (2017), pp. 5-12

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In the paper, we study equations in one variable over free semilattices. We show that the average number of solutions of a random equation over a free semilattice of a rank $n$ is equal to $\frac{3^n+2\cdot2^n}{3\cdot2^n}$. It is proved that the average number of irreducible components of algebraic sets defined by equations over a free semilattice of a countable rank is equal to 1.
Keywords: free semilattice, irreducible components.
Mots-clés : equation 
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     author = {M. A. Vakhrameev},
     title = {Random equations over free semilattices},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {5--12},
     publisher = {mathdoc},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2017_2_a0/}
}
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M. A. Vakhrameev. Random equations over free semilattices. Prikladnaâ diskretnaâ matematika, no. 2 (2017), pp. 5-12. http://geodesic.mathdoc.fr/item/PDM_2017_2_a0/