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Multi-triangulations as complexes of star polygons

Abstract : A $k$-triangulation of a convex polygon is a maximal set of diagonals so that no $k+1$ of them mutually cross. $k$-triangulations have received attention in recent literature, with motivation coming from several interpretations of them. We present a new way of looking at $k$-triangulations, where certain star polygons naturally generalize triangles for $k$-triangulations. With this tool we give new, direct proofs of the fundamental properties of $k$-triangulations (number of edges, definition of flip). This interpretation also opens up new avenues of research that we briefly explore in the last section.
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Vincent Pilaud, Francisco Santos. Multi-triangulations as complexes of star polygons. 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008), 2008, Viña del Mar, Chile. pp.319-330. ⟨hal-01185178⟩

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