Determinants from homomorphisms
Combinatorics
2022-04-25 v1 Computational Complexity
Data Structures and Algorithms
Abstract
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.
Keywords
Cite
@article{arxiv.2204.10718,
title = {Determinants from homomorphisms},
author = {Radu Curticapean},
journal= {arXiv preprint arXiv:2204.10718},
year = {2022}
}