On the kernel of tree incidence matrices
On the kernel of tree incidence matrices
复制标题
关于树关联矩阵的核
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
O. Golinelli
中科院分区：
文献类型：
--
作者：
M. Bauer;O. Golinelli
研究了随机树关联矩阵谱中0处的峰值高度。我们证明了一个大随机树中特征值0所占的谱的平均分数是渐近于2x-1 = 0.1342865808195677459999…其中x是x的唯一实根= exp（-x）对于有限树，我们给出了序列1,0,3,8,135,1164,21035,....的一个闭合形式，一个生成函数和一个渐近估计n^{n-2}树关联矩阵的集合中特征值0的总多重性的。
We study the height of the delta peak at 0 in the spectrum of random tree incidence matrices. We show that the average fraction of the spectrum occupied by the eigenvalue 0 in a large random tree is asymptotic to 2x-1 = 0.1342865808195677459999... where x is the unique real root of x = exp(-x). For finite trees, we give a closed form, a generating function, and an asymptotic estimate for the sequence 1,0,3,8,135,1164,21035,.... of the total multiplicity of the eigenvalue 0 in the set of n^{n-2} tree incidence matrices of size n>0.