A complete $g$-vector for convex polytopes

Abstract

We define an extension of the toric (middle perversity intersection homology) $g$-vector of a convex polytope $X$. The extended $g(X)$ encodes the whole of the flag vector $f(X)$ of $X$, and so is called complete. We find that for many examples that $g_k(X)\ge 0$ for most $k$ (independent of $X$).

3 pages. LaTeX

Cited by in corpus (2)

• Ring of Polytopes, Quasi-symmetric functions and Fibonacci numbers
• Axioms for the g-vector of general convex polytopes