A note on a-permanent and loop soup

摘要

In this paper, it is shown that a-permanent in algebra is closely related to loop soup in probability. We give explicit expansions of a-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.

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