Ron M. Adin, Marcelo Firer, Yuval Roichman
Published 2009-01-27Version 1
The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group $\widetilde{C}_n$ acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on $\widetilde{C}_n$. Lattice properties of this order are then applied to compute the diameter.
A conjecture on descents, inversions and the weak order
A combinatorial $\mathfrak{sl}_2$-action and the Sperner property for the weak order
Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$
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