Discrete & Computational Geometry

, Volume 12, Issue 4, pp 465–479 | Cite as

A decomposition of 2-weak vertex-packing polytopes

  • E. Steingrímsson


The 2-weak vertex-packing polytope of a loopless graphG withd vertices is the subset of the unitd-cube satisfyingx i +x j ≤1 for every edge (i,j) ofG. The dilation by 2 of this polytope is a polytope
with integral vertices. We triangulate
with lattice simplices of minimal volume and label the maximal simplices with elements of the hyperoctahedral groupB d . This labeling gives rise to a shelling of the triangulation
, where theh-vector of
(and the Ehrharth*-vector of
can be computed as a descent statistic on a subset ofB d defined in terms ofG. A recursive way of computing theh-vector of
is also given, and a recursive formula for the volume of


Convex Hull Simplicial Complex Recursive Formula Descent Statistic Permutation Statistic 


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Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • E. Steingrímsson
    • 1
  1. 1.Matematiska Institutionen CTH & GUGöteborgSweden

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