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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.04753 |
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| _version_ | 1866918073134481408 |
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| author | Chyzak, Frédéric Mishna, Marni |
| author_facet | Chyzak, Frédéric Mishna, Marni |
| contents | By a classic result of Gessel, the exponential generating functions for $k$-regular graphs are D-finite. Using Gröbner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regular graphs. The method is sufficiently robust to consider variants such as graphs with multiple edges, loops, and graphs whose degrees are limited to fixed sets of values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04753 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach Chyzak, Frédéric Mishna, Marni Combinatorics Symbolic Computation 05C30, 12H05 By a classic result of Gessel, the exponential generating functions for $k$-regular graphs are D-finite. Using Gröbner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regular graphs. The method is sufficiently robust to consider variants such as graphs with multiple edges, loops, and graphs whose degrees are limited to fixed sets of values. |
| title | Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach |
| topic | Combinatorics Symbolic Computation 05C30, 12H05 |
| url | https://arxiv.org/abs/2406.04753 |