2010/11/10 by Carl W. Lee, Lee, Carl W.
Mathematics · #52B05 #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #math.CO #msc:52B05
paper · pdf · doi:10.48550/arxiv.1011.2264
23 pages
arxiv created 2010/11/10 · openalex publication_date 2010/11/10 · arxiv updated 2010/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.