## 4 Citations

Multigraded commutative algebra of graph decompositions

- Mathematics
- 2014

The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar…

Noetherianity for infinite-dimensional toric varieties

- Mathematics
- 2013

We consider a large class of monomial maps respecting an action of the infinite symmetric group, and prove that the toric ideals arising as their kernels are finitely generated up to symmetry. Our…

Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs

- Computer Science, Mathematics
- 2014

A dynamic approach to explore the fiber of a model is presented, which is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models and allows for reciprocation effects.

## References

SHOWING 1-10 OF 10 REFERENCES

Degree Bounds for a Minimal Markov Basis for the Three-State Toric Homogeneous Markov Chain Model

- Mathematics
- 2011

We study the three state toric homogeneous Markov chain model and three special cases of it, namely: (i) when the initial state parameters are constant, (ii) without self-loops, and (iii) when both…

A Markov basis for two-state toric homogeneous Markov chain model without initial parameters

- Mathematics
- 2010

We derive a Markov basis consisting of moves of degree at most three for two-state toric homogeneous Markov chain model of arbitrary length without parameters for initial states. Our basis consists…

Markov degree of the three-state toric homogeneous Markov chain model

- Mathematics
- 2012

We consider the three-state toric homogeneous Markov chain model (THMC) without loops and initial parameters. At time $$T$$T, the size of the design matrix is $$6 \times 3\cdot 2^{T-1}$$6×3·2T-1 and…

Multigraded commutative algebra of graph decompositions

- Mathematics
- 2014

The toric fiber product is a general procedure for gluing two ideals, homogeneous with respect to the same multigrading, to produce a new homogeneous ideal. Toric fiber products generalize familiar…

Toric geometry of cuts and splits

- Mathematics
- 2006

Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and…

Cut ideals of K4-minor free graphs are generated by quadrics

- Mathematics
- 2008

Cut ideals are used in algebraic statistics to study statistical models defined by graphs. Intuitively, topological restrictions on the graphs should imply structural statements about the…

Ideals of Graph Homomorphisms

- Mathematics
- 2010

In combinatorial commutative algebra and algebraic statistics many toric ideals are constructed from graphs. Keeping the categorical structure of graphs in mind we give previous results a more…

Algebraic algorithms for sampling from conditional distributions

- Mathematics, Computer Science
- 1998

We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include contingency tables, logistic regression, and spectral…

Lectures on Algebraic Statistics

- Mathematics
- 2008

Markov Bases.- Likelihood Inference.- Conditional Independence.- Hidden Variables.- Bayesian Integrals.- Exercises.- Open Problems.