Geodesic
On recurrence relation in the problem of enumeration of finite posets
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 98-111

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In the previous paper of the author the formula reduced the count of the number $T_0(n)$ of posets defined on $n$-set to the calculation of the numbers $W(p_1,\ldots,p_k)$ of posets of a special form has been proved ($p_1+\ldots+p_k=n$). In present paper we obtain the relations of recurrent nature connecting the individual values of $W(p_1,\ldots,p_k)$ among themselves. As a result of these relations the partially folded formula for the number $T_0(n)$ is obtained.
Keywords: graph enumeration, poset, finite topology. 
@article{SEMR_2017_14_a2,
     author = {V. I. Rodionov},
     title = {On recurrence relation in the problem of enumeration of finite posets},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {98--111},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a2/}
}
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V. I. Rodionov. On recurrence relation in the problem of enumeration of finite posets. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 98-111. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a2/