The principal numbers of K. Saito for the types Al , Dl and El
- 作者：Yoshio Sano
- 关键词：Principal none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4N2D2WN-6&_mathId=mml27&_user=10&_cdi=5632&_rdoc=18&_acct=C000050221&_version=1&_userid=10&md5=797eae50971a6d7fdc5f8040f98699
- 刊名：Discrete Mathematics
- 出版年：2007
- 期刊代码：47_0012365x
- 类别：cp
- 出版时间：6 October 2007
- 卷：307
- 期：21
- 页码：2636-2642
- 文件大小：150 K
摘要
The principal number σ(Γ) for a tree Γ is introduced by K. Saito [Principal Γ-cone for a tree Γ, Adv. Math. (2007), to appear, (Available online 16 February 2007)] as the maximal number of chambers contained in components of the complement of the graphic arrangement attached to Γ (see Section 1).
The purpose of the present paper is to determine the principal numbers for the Coxeter–Dynkin graphs1 of types Al, Dl and El. We show that the generating series ,
and
satisfy certain differential equations of the first order. By solving the equations, we obtain the following results: