Combinatorics of binomial primary decomposition

By Alicia Dickenstein, Laura Felicia Matusevich, Ezra Miller. 2008

46 citations recorded by the source corpus.

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hypergeometric differential equations in several variables.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1dbaf7952fab6b1d82cff79c739bfb65ad1ce0b8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Thomas Kahle
2. Ezra Miller
3. Julianna Tymoczko

In Computational Theory and Mathematics

1. Thomas Kahle
2. Ezra Miller
3. Bernd Sturmfels
4. Huy Tài Hà
5. Arindam Banerjee
6. Adam Van Tuyl

In Geometry and Topology

1. Thomas Kahle
2. Ezra Miller
3. David Anderson
4. Allen Knutson
5. Julianna Tymoczko

Citations in the corpus

• Decompositions of binomial ideals (2009, methodology): “Dickenstein et al (2008) give an explicit lattice point characterization of binomial primary components, but it seems not easy to use these results for computation.”
• Decompositions of commutative monoid congruences and binomial ideals (2011, background): “That work covers ground anticipating — in a more general setting — the characterization of primary binomial ideals over algebraically closed fields of characteristic zero [Dickenstein et al. 2010b].”