Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910612527775744 |
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| author | Dreyfus, Thomas Price, Andrew Elvey Raschel, Kilian |
| author_facet | Dreyfus, Thomas Price, Andrew Elvey Raschel, Kilian |
| contents | In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on the complexity of the counting series. In this paper we introduce a unified approach based on the theory of elliptic functions, which allows us to have a common proof of the characterisation of the algebraicity and D-finiteness of the generating functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness Dreyfus, Thomas Price, Andrew Elvey Raschel, Kilian Combinatorics In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on the complexity of the counting series. In this paper we introduce a unified approach based on the theory of elliptic functions, which allows us to have a common proof of the characterisation of the algebraicity and D-finiteness of the generating functions. |
| title | Enumeration of weighted quadrant walks: criteria for algebraicity and D-finiteness |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.12806 |