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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2310.12812 |
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| _version_ | 1866912114715656192 |
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| author | Notarantonio, Hadrien Yurkevich, Sergey |
| author_facet | Notarantonio, Hadrien Yurkevich, Sergey |
| contents | In this article, we study systems of $n \geq 1$, not necessarily linear, discrete differential equations (DDEs) of order $k \geq 1$ with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions of such equations. This part of the present article can be seen as a generalization of the pioneering work by Bousquet-Mélou and Jehanne (2006) who settled down the case $n=1$. Moreover, we obtain effective bounds for the algebraicity degrees of the solutions and provide an algorithm for computing annihilating polynomials of the algebraic series. Finally, we carry out a first analysis in the direction of effectivity for solving systems of DDEs in view of practical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12812 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Systems of Discrete Differential Equations, Constructive Algebraicity of the Solutions Notarantonio, Hadrien Yurkevich, Sergey Combinatorics Computational Complexity In this article, we study systems of $n \geq 1$, not necessarily linear, discrete differential equations (DDEs) of order $k \geq 1$ with one catalytic variable. We provide a constructive and elementary proof of algebraicity of the solutions of such equations. This part of the present article can be seen as a generalization of the pioneering work by Bousquet-Mélou and Jehanne (2006) who settled down the case $n=1$. Moreover, we obtain effective bounds for the algebraicity degrees of the solutions and provide an algorithm for computing annihilating polynomials of the algebraic series. Finally, we carry out a first analysis in the direction of effectivity for solving systems of DDEs in view of practical applications. |
| title | Systems of Discrete Differential Equations, Constructive Algebraicity of the Solutions |
| topic | Combinatorics Computational Complexity |
| url | https://arxiv.org/abs/2310.12812 |