Determinants from Homomorphisms

Author Radu Curticapean

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Author Details

Radu Curticapean
  • IT University of Copenhagen, Denmark
  • Basic Algorithms Research Copenhagen, Denmark

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Radu Curticapean. Determinants from Homomorphisms. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 38:1-38:7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Linear algebra algorithms
  • Mathematics of computing → Combinatorics
  • Mathematics of computing → Graph theory
  • Theory of computation → Parallel algorithms
  • determinant
  • homomorphisms
  • matrix trace
  • Newton identities


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