Minimal primes of ideals arising from conditional independence statements

@article{Swanson2011MinimalPO,
  title={Minimal primes of ideals arising from conditional independence statements},
  author={Irena Swanson and Amelia Taylor},
  journal={Journal of Algebra},
  year={2011},
  volume={392},
  pages={299-314}
}
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References

SHOWING 1-10 OF 20 REFERENCES
Binomial edge ideals and conditional independence statements
Binomial Ideals
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many
Primary Decomposition of Lattice Basis Ideals
TLDR
All minimal primes in the 3  ×  n case are determined, and faster ways of computing a generating set for the associated toric ideal from a lattice basis ideal are presented.
Decompositions of binomial ideals
We present Binomials, a package for the computer algebra system Macaulay 2, which specializes well-known algorithms to binomial ideals. These come up frequently in algebraic statistics and
Robustness and Conditional Independence Ideals
We study notions of robustness of Markov kernels and probability distribution of a system that is described by $n$ input random variables and one output random variable. Markov kernels can be
Decompositions of Binomial Ideals in Macaulay 2
The package Binomials contains implementations of specialized algorithms for binomial ideals, including primary decomposition into binomial ideals. The current implementation works in characteristic
Graphs and Ideals Generated by Some 2-Minors
Let G be a finite graph on [n] = {1, 2,…, n}, X a 2 × n matrix of indeterminates over a field K, and S = K[X] a polynomial ring over K. In this article, we study about ideals I G of S generated by
Box-shaped Matrices and the Defining Ideal of Certain Blowup Surfaces
In this paper, we generalize the notions of a matrix and its ideal of 2 × 2 minors to that of a box-shaped matrix and its ideal of 2 × 2 minors, and make use of these notions to study projective
...
1
2
...