Determinants from homomorphisms

04/22/2022

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by   Radu Curticapean, et al.

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We give a new combinatorial explanation for well-known relations between determinants and traces of matrix powers. Such relations can be used to obtain polynomial-time and poly-logarithmic space algorithms for the determinant. Our new explanation avoids linear-algebraic arguments and instead exploits a classical connection between subgraph and homomorphism counts.