On the Kernel curves associated with walks in the quarter plane
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866929550480375808 |
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| author | Dreyfus, Thomas Hardouin, Charlotte Roques, Julien Singer, Michael F. |
| author_facet | Dreyfus, Thomas Hardouin, Charlotte Roques, Julien Singer, Michael F. |
| contents | The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve, this defines. In the present paper, we investigate the basic properties of the kernel curve (irreducibility, singularities, genus, uniformization, etc). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_01035 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Kernel curves associated with walks in the quarter plane Dreyfus, Thomas Hardouin, Charlotte Roques, Julien Singer, Michael F. Combinatorics 05A15, 30D05 The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve, this defines. In the present paper, we investigate the basic properties of the kernel curve (irreducibility, singularities, genus, uniformization, etc). |
| title | On the Kernel curves associated with walks in the quarter plane |
| topic | Combinatorics 05A15, 30D05 |
| url | https://arxiv.org/abs/2004.01035 |