Abstract:For affine Coxeter groups of affine types $\tilde D$ and $\tilde B$, we model the interval $[1,c]_T$ in the absolute order by symmetric noncrossing partitions of an annulus with one or two double points. In type $\tilde B$ (and \emph{almost} in type $\tilde D$), the diagrams also model the larger lattice defined by McCammond and Sulway.
| Comments: | 51 pages, 6 figures. Version 2: Small revisions and improvements throughout. Version 3: Small revisions and improvements, thanks to two anonymous referees. Version 4: final pre-publication version |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 20F55, 05E16 (Primary) 20F36 |
| Cite as: | arXiv:2312.17331 [math.CO] |
| (or arXiv:2312.17331v4 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2312.17331 arXiv-issued DOI via DataCite |
From: Nathan Reading [view email]
[v1]
Thu, 28 Dec 2023 19:13:31 UTC (155 KB)
[v2]
Fri, 13 Dec 2024 19:51:35 UTC (129 KB)
[v3]
Tue, 9 Dec 2025 21:00:36 UTC (134 KB)
[v4]
Thu, 21 May 2026 18:00:29 UTC (134 KB)
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