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arXiv · 2403.09408

A computer algebra package for bivariate asymptotics with explicit error terms

Benjamin Hackl·Stephan Wagner
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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.

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BibTeXRIS

Benjamin Hackl, Stephan Wagner. 2024-03-14. A computer algebra package for bivariate asymptotics with explicit error terms. https://doi.org/10.1016/j.tcs.2026.116011

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