论文标题
关于$α$ - 永久和循环汤的注释
A note on $α$-permanent and loop soup
论文作者
论文摘要
在本文中，表明代数的$α$ - 永久性与循环汤的可能性密切相关。我们给出了从相关的矩阵与$*$ - 森林相关的矩阵获得的$α$的$α$ - 内部的显式扩展，这些矩阵是一类包含Tridiagonal矩阵的特殊矩阵。这是通过两种方式证明的，一种是直接的组合证明，另一个是通过循环汤的概率证明。
In this paper, it is shown that $α$-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of $α$-permanents of the block matrices obtained from matrices associated to $*$-forests, which are a special class of matrices containing tridiagonal matrices. It is proved in two ways, one is the direct combinatorial proof, and the other is the probabilistic proof via loop soup.
