The work defines c-sortable biclosed sets in the affine symmetric group via pattern-avoiding TITOs and proves a bijection to c-noncrossing partitions using correspondences with arc diagrams and annular partitions.
A Garside presentation for Artin-Tits groups of type
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A generalization in affine type A of Coxeter sortable elements and Reading's bijection with noncrossing partitions
The work defines c-sortable biclosed sets in the affine symmetric group via pattern-avoiding TITOs and proves a bijection to c-noncrossing partitions using correspondences with arc diagrams and annular partitions.