3 citations · 14 across the 20 of their papers we have counts for
20 papers
Some stumbling first steps towards linear homology in a nutshell
Jonathan Fine
In 1985 Bayer and Billera defined a flag vector for every convex polytope , and proved some fundamental properties. The flag vectors span a graded ring $\mathcal{R…
The algebra of balanced dessins
Jonathan Fine
This paper gives a key definition, for a new approach to dessins and algebraic numbers. The distant goal is to construct from each dessin an algebraic number , in a system…
Bias and dessins
Jonathan Fine
Grothendieck's theory of dessins provides a bridge between algebraic numbers and combinatorics. This paper adds a new concept, called 'bias', to the bridge. This produces: (i) from…
Axioms for the g-vector of general convex polytopes
Jonathan Fine
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 dimensi…
A complete -vector for convex polytopes
Jonathan Fine
We define an extension of the toric (middle perversity intersection homology) -vector of a convex polytope . The extended encodes the whole of the flag vector o…
A complete h-vector for convex polytopes
Jonathan Fine
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…