Minimal Betti Numbers
Minimal Betti Numbers
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最小贝蒂数
DOI：
10.1080/00927870601115617
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发表时间：
2006
影响因子：
0.7
通讯作者：
Benjamin P. Richert
中科院分区：
文献类型：
--
作者：
Christopher Dodd;Andrew S. Marks;Victor Meyerson;Benjamin P. Richert
给出了无平方根单项理想的（分次）Betti数的极值行为的判定条件.对于非唯一极小值的情况下，我们给出了几个条件，我们用来产生无限的家庭，指数增长的维度，Hilbert函数，其中没有最小的（分次）Betti数之间的squarefree单项理想和所有的理想。对于唯一极小的情况下，我们给出了两个家庭的Hilbert函数，一个指数和线性增长的维数的增长，有唯一的最小Betti数之间的平方自由单项理想。
We give conditions for determining the extremal behavior for the (graded) Betti numbers of squarefree monomial ideals. For the case of non-unique minima, we give several conditions which we use to produce infinite families, exponentially growing with dimension, of Hilbert functions which have no smallest (graded) Betti numbers among squarefree monomial ideals and all ideals. For the case of unique minima, we give two families of Hilbert functions, one with exponential and one with linear growth as dimension grows, that have unique minimal Betti numbers among squarefree monomial ideals.