Abstract
The 2-weak vertex-packing polytope of a loopless graphG withd vertices is the subset of the unitd-cube satisfyingxi+xj≤1 for every edge (i,j) ofG. The dilation by 2 of this polytope is a polytope[Figure not available: see fulltext.] with integral vertices. We triangulate[Figure not available: see fulltext.] with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral groupBd. This labeling gives rise to a shelling of the triangulation[Figure not available: see fulltext.] of[Figure not available: see fulltext.], where theh-vector of[Figure not available: see fulltext.] (and the Ehrharth*-vector of[Figure not available: see fulltext.] can be computed as a descent statistic on a subset ofBd defined in terms ofG. A recursive way of computing theh-vector of[Figure not available: see fulltext.] is also given, and a recursive formula for the volume of[Figure not available: see fulltext.].
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