On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley
On the degree two entry of a Gorenstein h-vector and a conjecture of Stanley
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关于 Gorenstein h 向量的二次项和 Stanley 猜想
DOI：
10.1090/s0002-9939-08-09456-2
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
Fabrizio Zanello
中科院分区：
文献类型：
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作者：
J. Migliore;U. Nagel;Fabrizio Zanello
在这个简短的纸,我们建立一个(简单的)下限的程度两个条目h 2戈伦斯坦h-vector任何给定的脚柱度e和任何余维数r。特别是,当e = 4,也就是说,表单的戈伦斯坦h-vectors h = (1 r h 2 r, 1),下界允许我们来证明猜想斯坦利的最小值的数量级,说f (r), h 2可能假设。事实上，我们证明了limr→∞f(r) r 2/3 =6 2/3。一般来说，我们想知道对于所有整数，我们的下界是否锐利。
In this short paper we establish a (non-trivial) lower bound on the degree two entry h 2 of a Gorenstein h-vector of any given socle degree e and any codimension r. In particular, when e = 4, that is, for Gorenstein h-vectors of the form h = (1, r, h 2 , r, 1), our lower bound allows us to prove a conjecture of Stanley on the order of magnitude of the minimum value, say f(r), that h 2 may assume. In fact, we show that limr→∞ f(r) r 2/3 =6 2/3 . In general, we wonder whether our lower bound is sharp for all integers e > 4 and r > 2.