A computer algebra package for bivariate asymptotics with explicit error terms
Abstract
Making use of a newly developed package in the computer mathematics system SageMath, we show how to perform a full asymptotic analysis of certain types of sums that occur frequently in combinatorics, including explicit error bounds. We present two applications of the general approach to illustrate its use: the first concerns a classical problem due to Ramanujan, while the second one concerns a question of B\'ona and DeJonge on 132-avoiding permutations with a unique longest increasing subsequence that can be translated into an inequality for a certain binomial sum.
Cite
@article{arxiv.2403.09408,
title = {A computer algebra package for bivariate asymptotics with explicit error terms},
author = {Benjamin Hackl and Stephan Wagner},
journal= {arXiv preprint arXiv:2403.09408},
year = {2025}
}
Comments
Full version of extended abstract presented at the 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024), published in proceedings at https://doi.org/10.4230/LIPIcs.AofA.2024.19