Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917020152365056 |
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| author | Orevkov, Stepan |
| author_facet | Orevkov, Stepan |
| contents | Let $f(m,n)$ be the number of primitive lattice triangulations of an $m \times n$ rectangle. We express the limits $\lim_n f(m,n)^{1/n}$ for $m = 4$ and $m=5$ in terms of certain systems of Fredholm integral equations on generating functions (the case $m\le3$ was treated in a previous paper). Solving these equations numerically, we compute approximate values of these limits with a rather high precision. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5 Orevkov, Stepan Combinatorics Let $f(m,n)$ be the number of primitive lattice triangulations of an $m \times n$ rectangle. We express the limits $\lim_n f(m,n)^{1/n}$ for $m = 4$ and $m=5$ in terms of certain systems of Fredholm integral equations on generating functions (the case $m\le3$ was treated in a previous paper). Solving these equations numerically, we compute approximate values of these limits with a rather high precision. |
| title | Asymptotics of the number of lattice triangulations of rectangles of width 4 and 5 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2412.17065 |