A computer algebra package for bivariate asymptotics with explicit error terms
arXiv:2403.09408 · doi:10.1016/j.tcs.2026.116011
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 Bóna and DeJonge on 132-avoiding permutations with a unique longest increasing subsequence that can be translated into an inequality for a certain binomial sum.
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