Deformed graphical zonotopal algebras
Boris Shapiro, Ilya Smirnov, Arkady Vaintrob
TL;DR
This paper investigates a class of deformed algebraic structures associated with graphs, exploring their properties, computing their Hilbert series for various cases, and proposing conjectures about their behavior.
Contribution
It introduces filtered deformations of external zonotopal algebras parametrized by polynomials and analyzes their properties and Hilbert series.
Findings
Established general properties of the deformed algebras
Computed Hilbert series for multiple graphs using Macaulay2
Formulated several conjectures about the algebraic structures
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models