Kirchhoff's theorem is a mathematical theorem that states the number of spanning trees in a graph can be calculated from the determinant of a submatrix of the Laplacian matrix. It is a generalization of Cayley's formula which provides the number of spanning trees in a complete graph.

Stanford University

Autumn 2022

The course addresses both classic and recent developments in counting and sampling. It covers counting complexity, exact counting via determinants, sampling via Markov chains, and high-dimensional expanders.

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