2010/11/18 by Jonathan Fine, Fine, Jonathan
Mathematics · #52B11 (Primary) 55N33 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:52B11 #msc:55N33
paper · pdf · doi:10.48550/arxiv.1011.4269
LaTeX2e. 10 pages
arxiv created 2010/11/18 · arxiv updated 2010/11/19
McMullen's g-vector is important for simple convex polytopes. This paper postulates axioms for its extension to general convex polytopes. It also conjectures that, for each dimension d, a stated finite calculation gives the formula for the extended g-vector. This calculation is done by computer for d=5 and the results analysed. The conjectures imply new linear inequalities on convex polytope flag vectors. Underlying the axioms is a hypothesised higher-order homology extension to middle perversity intersection homology (order-zero homology), which measures the failure of lower-order homology to have a ring structure.