A computer algebra package for bivariate asymptotics with explicit error terms
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915193091522560 |
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| author | Hackl, Benjamin Wagner, Stephan |
| author_facet | Hackl, Benjamin Wagner, Stephan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_09408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A computer algebra package for bivariate asymptotics with explicit error terms Hackl, Benjamin Wagner, Stephan Combinatorics Discrete Mathematics Mathematical Software 05A15, 05A16, 05-04 G.2.1; G.4 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. |
| title | A computer algebra package for bivariate asymptotics with explicit error terms |
| topic | Combinatorics Discrete Mathematics Mathematical Software 05A15, 05A16, 05-04 G.2.1; G.4 |
| url | https://arxiv.org/abs/2403.09408 |