A decomposition of 2-weak vertex-packing polytopes
- 57 Downloads
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 with integral vertices. We triangulate 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 of, where theh-vector of (and the Ehrharth*-vector of can be computed as a descent statistic on a subset ofBd defined in terms ofG. A recursive way of computing theh-vector of is also given, and a recursive formula for the volume of.
Unable to display preview. Download preview PDF.
- 3.A. Björner: Topological methods,Handbook of combinatorics (R. Graham, M. Grötschel, and L. Lovász, eds.), North-Holland, Amsterdam, to appear.Google Scholar
- 5.J. Lee and W. D. Morris, Geometric comparison of combinatorial polytopes, CORE Discussion Paper 9216, 1992.Google Scholar
- 13.R. Stanley: Generalizedh-vectors, intersection cohomology of toric varieties, and related results,Commutative Algebra and Combinatorics, Advanced Studies in Pure Mathematics, Vol. 11, 1987, pp. 187–213.Google Scholar
- 14.E. Steingrímsson: Permutation statistics of indexed and poset permutations, Ph.D. thesis, Massachusetts Institute of Technology, 1991.Google Scholar
- 15.E. Steingrímsson: Weak vertex-packing polytopes, Preprint 1993:19, Matematiska Institutionen CTH & GU.Google Scholar
© Springer-Verlag New York Inc. 1994