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math.CO2025
Oriented matroids from type cluster categories
Nicholas J. Williams
For any cluster-tilting object in the cluster category of type , we construct a rank-four oriented matroid …
math.CO2025
Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
Mikhail Gorsky, Nicholas J. Williams
We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotien…