Differential algebraic generating series of weighted walks in the quarter plane
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866914979177824256 |
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| author | Dreyfus, Thomas |
| author_facet | Dreyfus, Thomas |
| contents | In the present paper we study the nature of the trivariate generating series of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we complete the proof of the following theorem. The series satisfies a nontrivial algebraic differential equation in one of its variable, if and only if it satisfies a nontrivial algebraic differential equation in each of its variables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05505 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Differential algebraic generating series of weighted walks in the quarter plane Dreyfus, Thomas Combinatorics 05A15, 30D05, 39A06 In the present paper we study the nature of the trivariate generating series of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we complete the proof of the following theorem. The series satisfies a nontrivial algebraic differential equation in one of its variable, if and only if it satisfies a nontrivial algebraic differential equation in each of its variables. |
| title | Differential algebraic generating series of weighted walks in the quarter plane |
| topic | Combinatorics 05A15, 30D05, 39A06 |
| url | https://arxiv.org/abs/2104.05505 |