Symmetric noncrossing partitions of an annulus with double points

Nathan Reading

Symmetric noncrossing partitions of an annulus with double points

Combinatorics 2026-05-25 v4

Authors: Nathan Reading

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.

Keywords

affine Coxeter groups symmetric noncrossing partitions annulus double points absolute order lattice

Cite

@article{arxiv.2312.17331,
  title  = {Symmetric noncrossing partitions of an annulus with double points},
  author = {Nathan Reading},
  journal= {arXiv preprint arXiv:2312.17331},
  year   = {2026}
}

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

Symmetric noncrossing partitions of an annulus with double points

Abstract

Keywords

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