Asymptotics of Redistricting the $n\times n$ Grid
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909390182809600 |
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| author | Donnay, Christopher Kahle, Matthew |
| author_facet | Donnay, Christopher Kahle, Matthew |
| contents | Redistricting is the act of dividing a region into districts for electoral representation. Motivated by this application, we study two questions. How many ways are there to partition the $n\times n$ grid into $n$ contiguous districts of equal size? How many of these partitions are ``compact"? We give asymptotic bounds on the number of plans: a lower bound of roughly $1.41^{n^2}$ and an upper bound of roughly $3.21^{n^2}$. We then use the lower bound to show that most plans are not compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13550 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Asymptotics of Redistricting the $n\times n$ Grid Donnay, Christopher Kahle, Matthew Combinatorics 05A02 (Primary) 05C02 (Secondary) Redistricting is the act of dividing a region into districts for electoral representation. Motivated by this application, we study two questions. How many ways are there to partition the $n\times n$ grid into $n$ contiguous districts of equal size? How many of these partitions are ``compact"? We give asymptotic bounds on the number of plans: a lower bound of roughly $1.41^{n^2}$ and an upper bound of roughly $3.21^{n^2}$. We then use the lower bound to show that most plans are not compact. |
| title | Asymptotics of Redistricting the $n\times n$ Grid |
| topic | Combinatorics 05A02 (Primary) 05C02 (Secondary) |
| url | https://arxiv.org/abs/2311.13550 |