Dihedral Graph Properties
We discuss monotone dihedral graph properties, which are graph complexes on [n]that are invariant under the natural action of the dihedral group D n . More precisely, identify the corners of a regular n-gon with the vertices 1,…, n arranged in clockwise direction. Representing a given edge ij with the open line segment between the points representing i and j, we obtain the polygon representation of a graph. The natural action of D n on this graph is simply the action induced by the natural action of D n on the n—gon.
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