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Working paper

Operators of rank 1, discrete path integration and graph Laplacians

arxiv.org. math. Cornell University, 2012. No. arXiv:1205.1123.

We calculate characteristic polynomials of operators explicitly represented as polynomials of rank $1$ operators. Applications of the results obtained include a generalization of the Forman--Kenyon's formula for a determinant of the graph Laplacian and also provide its level $2$ analog involving summation over triangulated nodal surfaces with boundary.