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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2212.13799 |
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| _version_ | 1866913150336499712 |
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| author | Reading, Nathan |
| author_facet | Reading, Nathan |
| contents | We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_13799 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Noncrossing partitions of a marked surface Reading, Nathan Combinatorics We define noncrossing partitions of a marked surface without punctures (interior marked points). We show that the natural partial order on noncrossing partitions is a graded lattice and describe its rank function topologically. Lower intervals in the lattice are isomorphic to products of noncrossing partition lattices of other surfaces. We similarly define noncrossing partitions of a symmetric marked surface with double points and prove some of the analogous results. The combination of symmetry and double points plays a role that one might have expected to be played by punctures. |
| title | Noncrossing partitions of a marked surface |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2212.13799 |