293 citations · 737 across the 36 of their papers we have counts for
9 papers · 1 filter
Conditional independence ideals with hidden variables
Oliver Clarke, Fatemeh Mohammadi, Johannes Rauh
We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditio…
The Markov basis of
Johannes Rauh, Seth Sullivant
This document explains how to obtain a Markov basis of the graphical model of the complete bipartite graph with binary nodes. The computations illustrate the theory devel…
Lifting Markov Bases and Higher Codimension Toric Fiber Products
Johannes Rauh, Seth Sullivant
We study how to lift Markov bases and Gröbner bases along linear maps of lattices. We give a lifting algorithm that allows to compute such bases iteratively provided a certain asso…
Toric fiber products versus Segre products
Thomas Kahle, Johannes Rauh
The toric fiber product is an operation that combines two ideals that are homogeneous with respect to a grading by an affine monoid. The Segre product is a related construction tha…
Generalized Binomial Edge Ideals
Johannes Rauh
This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional ind…
Prime splittings of Determinantal Ideals
Fatemeh Mohammadi, Johannes Rauh
We consider determinantal ideals, where the generating minors are encoded in a hypergraph. We study when the generating minors form a Gröbner basis. In this case, the ideal is radi…