Convex polytopes and linear algebra

1997/10/01 by Jonathan Fine, Fine, Jonathan
Engineering · Mathematics · #14M25 #15A69 #52B05 #55N33 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #alg-geom #graph theory and CDMA systems #math.AG #msc:14M25 #msc:15A69 #msc:52B05 #msc:55N33

paper · pdf · doi:10.48550/arxiv.alg-geom/9710001

LaTeX2e. 14 pages

arxiv created 1997/10/01 · openalex publication_date 1997/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper defines, for each convex polytope Δ, a family H_wΔ of vector spaces. The definition uses a combination of linear algebra and combinatorics. When what is called exact calculation holds, the dimension h_wΔ of H_wΔ is a linear function of the flag vector fΔ. It is expected that the H_wΔ are examples, for toric varieties, of the new topological invariants introduced by the author in "Local-global intersection homolog" (preprint alg-geom/9709011).

Related

• A complete g-vector for convex polytopes
• A complete h-vector for convex polytopes
• Axioms for the g-vector of general convex polytopes
• Sweeping the cd-Index and the Toric h-Vector
• Ring structure, uniform expressions and intersection homology