Toric fiber products
By Seth Sullivant. 2006
96 citations recorded by the source corpus.
Abstract We introduce and study the toric fiber product of two ideals in polynomial rings that are homogeneous with respect to the same multigrading. Under the assumption that the set of degrees of the variables form a linearly independent set, we can explicitly describe generating sets and Grobner bases for these ideals. This allows us to unify and generalize some results in algebraic statistics.
Subfields: Algebra and Number Theory, Computational Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/a8145a1914948837ab31b4f24fd4c1bad476076d
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In Algebra and Number Theory
- Bernd Sturmfels
- Seth Sullivant
- Lindsay C. Piechnik
- Francisco Santos
- Christian Haase
- Andreas Paffenholz
- Adam Van Tuyl
- Eric Katz
In Computational Mathematics
In Computational Theory and Mathematics
- Bernd Sturmfels
- Seth Sullivant
- Lindsay C. Piechnik
- Francisco Santos
- Christian Haase
- Andreas Paffenholz
- Federico Ardila
- Adam Van Tuyl
Citations in the corpus
- Toric geometry of cuts and splits (2006, methodology): “Specifically, we shall identify the cut ideal of G = G1#G2 as a toric fiber product. We begin by reviewing the set-up of [ 21 ].”
- Existence of unimodular triangulations — positive results (2014, background): “It was subsequently also proven by Ohsugi and Hibi [84] and by Sullivant [117].”