Combinatorics and geometry of power ideals

  title={Combinatorics and geometry of power ideals},
  author={Alexander Postnikov},
We investigate ideals in a polynomial ring which are generated by powers of linear forms. Such ideals are closely related to the theories of fat point ideals, Cox rings, and box splines. We pay special attention to a family of power ideals that arises naturally from a hyperplane arrangement A. We prove that their Hilbert series are determined by the combinatorics of A and can be computed from its Tutte polynomial. We also obtain formulas for the Hilbert series of certain closely related fat… CONTINUE READING
Highly Cited
This paper has 36 citations. REVIEW CITATIONS


Publications referenced by this paper.
Showing 1-10 of 30 references

Hyperplane arrangements

  • R. Stanley
  • In Geometric Combinatorics (E. Miller, V. Reiner…
  • 2007

Zonotopal algebra

  • O. Holtz, A. Ron
  • Preprint,
  • 2007

Rota . The umbral calculus

  • C. G.
  • Beiträge Algebra Geom .
  • 2006

The algebra of the box spline

  • C. De Concini, C. Procesi
  • Preprint,
  • 2006

The umbral calculus . Adv . in Math . 27 (

  • S. Roman, G. C. Rota
  • Beiträge Algebra Geom
  • 2006

Sokal . The multivariate Tutte polynomial ( alias Potts model ) for graphs and matroids

  • A.
  • Surveys in Combinatorics
  • 2005

Similar Papers

Loading similar papers…