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Statistics of perfect matching and incremental perfect matchings in bipartite planar graphs?
Planar graph permanent can be reduced to determinants and so statistics should be amenable.
Pick a uniformly random bipartite planar graph $G$ with $n$ vertices of each color and choose new additional ...
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Is there a bipartite graph whose determinant corresponds to number of perfect matchings?
Let $M\in\{0,1\}^{n\times n}$ be a square integer matrix. If we consider $M$ as biadjacency of a balanced bipartite graph on $2n$ vertices having $n$ vertices of color $1$ and $n$ vertices of color $2$...