Defines flips and mutations on posets and lattices, proves mutable lattices are semidistributive, establishes local mutability for type-A and type-B Cambrian lattices, and introduces Ordovician lattices via iterated mutations with conjectures on their structure and cluster algebra compatibility.
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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.
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Flip of lattices
Defines flips and mutations on posets and lattices, proves mutable lattices are semidistributive, establishes local mutability for type-A and type-B Cambrian lattices, and introduces Ordovician lattices via iterated mutations with conjectures on their structure and cluster algebra compatibility.
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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.