色分拆恒等式的Graver基与泛Gröbner基的等价性
Equality of Graver bases and universal Gröbner bases of colored partition identities
摘要：
与任何向量配置A相关联的是由A的核中的向量编码的复曲面理想。每个复曲面理想都有两个特殊的生成集：泛Gröbner基和Graver基。虽然前者通常是后者的真子集，但也有两个集合重合的情况。其中最突出的例子是幺模矩阵的环面理想。泛Gröbner基和Graver基的相等性是复曲面理想（或定义矩阵）的一个组合性质，提供了关于矩阵的高阶Lawrence提升理想的有趣信息。尽管如此，这两个集合都同意的所有矩阵的一般分类还远未可知。我们有助于这一任务，确定所有的情况下，平等的两个家庭的矩阵，即那些定义合理的正常涡卷和那些编码同质原始着色分区身份。
英文摘要：
Associated to any vector configuration A is a toric ideal encoded by vectors in the kernel of A. Each toric ideal has two special generating sets: the universal Gröbner basis and the Graver basis. While the former is generally a proper subset of the latter, there are cases for which the two sets coincide. The most prominent examples among them are toric ideals of unimodular matrices. Equality of universal Gröbner basis and Graver basis is a combinatorial property of the toric ideal (or, of the defining matrix), providing interesting information about ideals of higher Lawrence liftings of a matrix. Nonetheless, a general classification of all matrices for which both sets agree is far from known. We contribute to this task by identifying all cases with equality within two families of matrices; namely, those defining rational normal scrolls and those encoding homogeneous primitive colored partition identities.
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