English

Sweeping the cd-Index and the Toric h-Vector

Combinatorics 2010-11-11 v1

Abstract

We derive formulas for the cd-index and the toric h-vector of a convex polytope P from a sweeping by a hyperplane. These arise from interpreting the corresponding S-shelling of the dual of P. We describe a partition of the faces of the complete truncation of P to reflect explicitly the nonnegativity of its cd-index and what its components are counting. One corollary is a quick way to compute the toric h-vector directly from the cd-index. We also propose an "extended toric" h-vector that fully captures the information in the flag h-vector.

Cite

@article{arxiv.1011.2264,
  title  = {Sweeping the cd-Index and the Toric h-Vector},
  author = {Carl W. Lee},
  journal= {arXiv preprint arXiv:1011.2264},
  year   = {2010}
}

Comments

23 pages

R2 v1 2026-06-21T16:41:33.704Z