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Triangle-free triangulations. (English) Zbl 1278.05245

Summary: The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group \(\tilde C _n\) 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 \(\tilde C _n\). Lattice properties of this order are then applied to compute the diameter.

MSC:

05E18 Group actions on combinatorial structures
06B05 Structure theory of lattices
20F55 Reflection and Coxeter groups (group-theoretic aspects)
52B70 Polyhedral manifolds
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References:

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