A complete h-vector for convex polytopes

Details A complete h-vector for convex polytopes A complete h-vector for convex polytopes

2009-11-30

arxiv.org/abs/0911.5722v1

Mathematics

Combinatorics

4 pages, LaTeX, no figures

Scientific paper

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.

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