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摘要翻译：
我们引入了代数统计中的等变树模型，它统一和推广了现有的树模型，如一般马尔可夫模型、串对称模型和基于群的模型。我们专注于这类模型的理想。我们展示了如何从星的理想中确定一般树的理想。主要的新奇之处在于我们证明了这个过程产生了整个理想，而不仅仅是一个理论上定义模型集的理想。一个理论上重要的推论是，一般树的理想是由它在顶点的扁平的理想产生的。
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英文标题：
《On the ideals of equivariant tree models》
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作者：
Jan Draisma and Jochen Kuttler
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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. We focus on the ideals of such models. We show how the ideals for general trees can be determined from the ideals for stars. The main novelty is our proof that this procedure yields the entire ideal, not just an ideal defining the model set-theoretically. A corollary of theoretical importance is that the ideal for a general tree is generated by the ideals of its flattenings at vertices.
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PDF链接：
https://arxiv.org/pdf/0712.3230
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