2009/11/30 by Jonathan Fine, Fine, Jonathan
Mathematics · #52B11 (Primary) #55N33 (Secondary) #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.CO #msc:52B11 #msc:55N33
paper · pdf · doi:10.48550/arxiv.0911.5722
4 pages, LaTeX, no figures
arxiv created 2009/11/30 · openalex publication_date 2009/11/30 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note defines a complete h-vector for convex polytopes, which extends the already known toric (or mpih) h-vector and has many similar properties. Complete means that it encodes the whole of the flag vector. First we define the concept of a generalised h-vector and state some properties that follow. The toric h-vector is given as an example. We then define a complete generalised h-vector, and again state properties. Finally, we show that this complete h-vector and all with similar properties will sometimes have negative coefficients. Most of the proofs, and further investigations, will appear elsewhere.