Geodesic
On the cardinality of layers in even-valued $n$-dimensional lattice
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 2, pp. 153-169 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, we explicitly calculated terms additional to the main one of cardinality asymptotics of central layers in the $n$-dimensional $k$-valued lattice $E^n_k$ for even $k$ as $n\to\infty$. The main term had been found by V.B. Alekseev for a certain class of posets. The case of odd $k$, which is technically less complicated, was the major focus of our previous work.
Keywords: poset, layer, asymptotics, generating function. 
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     title = {On the cardinality of layers in even-valued $n$-dimensional lattice},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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T. V. Andreeva; Yu. S. Semenov. On the cardinality of layers in even-valued $n$-dimensional lattice. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 164 (2022) no. 2, pp. 153-169. http://geodesic.mathdoc.fr/item/UZKU_2022_164_2_a0/

[1] Andreeva T.V., Semenov Yu.S., “On the cardinality of layers in some partially ordered sets”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 162:3 (2020), 269–284 (In Russian) | DOI

[2] Alekseev V.B., “On the number of $k$-valued monotone functions”, Probl. Kibern., 28, 1974, 5–24 (In Russian)

[3] Dwight H.B., Tables of Integrals and Other Mathematical Data, Nauka, M., 1978, 224 pp. (In Russian)