On the ideals of equivariant tree models
By Jan Draisma, J. Kuttler. 2007
80 citations recorded by the source corpus.
We introduce equivariant tree models in algebraic statistics, which unify and generalise existing tree models such as the general Markov model, the strand symmetric model, and group-based models such as the Jukes–Cantor and Kimura models. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices. The main novelty is that our results yield generators of the full ideal rather than an ideal which only defines the model set-theoretically.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/1fd52f45b48c4c175fc11e8378e72b72610793da
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Bounded-rank tensors are defined in bounded degree (2011, background): “Indeed, in [2] it is proved that the k-state general Markov model on any tree is cut out by certain (k+1)×(k+1)-determinants together with the equations coming from star models (and this also holds scheme-theoretically [15]).”