Deformed graphical zonotopal algebras

Abstract

We study certain filtered deformations of the external zonotopal algebra of a given graph parametrized by univariate polynomials. We establish some general properties of these algebras, compute their Hilbert series for a number of graphs using Macaulay2, and formulate several conjectures.

23 pages, 12 pictures. The new version fixes some minor mistakes including a new formulation of Conjecture 5.1 proven in a recent preprint arXiv: 2207.10605. The title is changed to better reflect the content of the paper