Rationality and reciprocity for the greedy normal form of a Coxeter group
Rationality and reciprocity for the greedy normal form of a Coxeter group
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Coxeter 群贪婪范式的有理性和互惠性
DOI：
10.1090/s0002-9947-2010-05093-7
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发表时间：
2008
影响因子：
1.3
通讯作者：
R. Scott
中科院分区：
文献类型：
--
作者：
R. Scott
证明了Coxeter群的贪婪标准形的特征级数总是有理级数，并证明了当群是直角群且神经是欧拉群时该级数的一个互易公式.作为推论，我们得到了许多已知的合理性和互惠性的结果，以及一些新的Coxeter群的增长序列。
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series of Coxeter groups as well as some new ones.