Flag subdivisions and γ-vectors
Flag subdivisions and γ-vectors
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DOI：
10.2140/pjm.2012.259.257
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发表时间：
2012-10
影响因子：
0.6
通讯作者：
Christos A. Athanasiadis
中科院分区：
文献类型：
--
作者：
Christos A. Athanasiadis
向量是旗单同调球面的一个重要的计数不变量。Gal证明了这个向量对每一个这样的球面1都是非负的，Reiner、Postnikov和威廉姆斯证明了当1被任何几何上细分了1的旗单纯同调球面所取代时，这个向量会增加。使用非负性的-向量在3维，证明戴维斯和奥肯，以及斯坦利的理论单纯细分和当地的h-向量，后者的猜想证实了本文在3和4维。
The -vector is an important enumerative invariant of a flag simplicial homology sphere. It has been conjectured by Gal that this vector is nonnegative for every such sphere 1 and by Reiner, Postnikov and Williams that it increases when1 is replaced by any flag simplicial homology sphere that geometrically subdivides1. Using the nonnegativity of the -vector in dimension 3, proved by Davis and Okun, as well as Stanley’s theory of simplicial subdivisions and local h-vectors, the latter conjecture is confirmed in this paper in dimensions 3 and 4.