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11 votes
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Analogue of conic sections for the permutohedra, associahedra, and noncrossing partitions

Slicing cones in various ways with a plane generates conic sections identified geometrically as hyperbolas, parabolas, or ellipses and algebraically, when suitably rotated, as certain rescaled ...
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5 votes
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Cataland: Facets and partition polynomials of cluster complexes

Figure 25 on pg. 101 of "Cataland: Why the Fuss?" by Christian Stump, Hugh Thomas, and Nathan Williams depicts cluster complexes (CCs) associated with generalized $(m)$-Narayana / ...
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