On the ideals of equivariant tree models

J. Draisma, J. Kuttler

Research output: Contribution to journalArticleAcademicpeer-review

42 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)619-644
JournalMathematische Annalen
Volume344
Issue number3
DOIs
Publication statusPublished - 2009

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