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
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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.
@article{UZKU_2022_164_2_a0,
author = {T. V. Andreeva and Yu. S. Semenov},
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},
pages = {153--169},
publisher = {mathdoc},
volume = {164},
number = {2},
year = {2022},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2022_164_2_a0/}
}
TY - JOUR AU - T. V. Andreeva AU - Yu. S. Semenov TI - On the cardinality of layers in even-valued $n$-dimensional lattice JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2022 SP - 153 EP - 169 VL - 164 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2022_164_2_a0/ LA - ru ID - UZKU_2022_164_2_a0 ER -
%0 Journal Article %A T. V. Andreeva %A Yu. S. Semenov %T On the cardinality of layers in even-valued $n$-dimensional lattice %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2022 %P 153-169 %V 164 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2022_164_2_a0/ %G ru %F UZKU_2022_164_2_a0
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/