Axioms for the g-vector of general convex polytopes

Details Axioms for the g-vector of general convex polytopes Axioms for the g-vector of general convex polytopes

2010-11-18

arxiv.org/abs/1011.4269v1

Mathematics

Combinatorics

LaTeX2e. 10 pages

Scientific paper

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.

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