Matching generating function
= Matching generating function
{title2=$Z_G(\lambda)=\sum_k m_k\lambda^k$}
The coefficient $m_k$ counts <matchings in a graph> with $k$ <edges>. For a <bipartite graph> with $n$ <vertices> on each side, $m_n$ counts <perfect matchings> and equals the <permanent of a matrix> of its bipartite adjacency <matrix>. Positive activity $\lambda$ makes $Z_G$ the normalizing constant of the <weighted matching Markov chain>.