On the asymptotics of the coefficients of some generating functions

Recieved: 08/05/2024

Accepted: 09/03/2024

Published: 01/31/2025

Keywords: generating function; partially ordered set

Available in the on-line version with: 31.01.2025

To cite this article

Andreeva T. V., Liu Yo. On the asymptotics of the coefficients of some generating functions. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics 2025. N 1. p.3-9 https://doi.org/10.55959/MSU/0137–0782–15–2025–49–1–3–9.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Andreeva T. V. (Lomonosov Moscow State University (MSU))
Liu Yo. (Lomonosov Moscow State University (MSU))

Abstract

In the article, the asymptotics of the coefficients of the generating functions are found with a certain accuracy, which can be used to calculate the powers of layers of certain types of partially ordered sets, as well as to calculate the values of the sums of boundary functionals when estimating the number of antichains in such sets. In addition, applications of the obtained results are considered using examples.