The Hilbert Series of the Face Ring of a Flag Complex
The Hilbert Series of the Face Ring of a Flag Complex
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旗面环的希尔伯特级数综合体
DOI：
10.1007/s003730200045
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
P. Renteln
中科院分区：
文献类型：
--
作者：
P. Renteln
结果表明，graphGis 的派系复合体（相当于标志复合体）的面环的希尔伯特级数，最多为一个因子，只是 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} 的特化\usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}，G 的补集的子图多项式。 We also find a simple relationship between the size of a minimum vertex cover of a graphGand its subgraph polynomial.这根据 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} 的两个不变量生成标志复合体的 h 向量公式\begin{文档}\end{文档}。 Some computational issues are addressed and a recursive formula for the Hilbert series is given based on an algorithm of Bayer and Stillman.
It is shown that the Hilbert series of the face ring of a clique complex (equivalently, flag complex) of a graphGis, up to a factor, just a specialization of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}, the subgraph polynomial of the complement ofG. We also find a simple relationship between the size of a minimum vertex cover of a graphGand its subgraph polynomial. This yields a formula for theh-vector of the flag complex in terms of those two invariants of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}. Some computational issues are addressed and a recursive formula for the Hilbert series is given based on an algorithm of Bayer and Stillman.
DOI：
--
发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
--
作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest