License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2022.38
URN: urn:nbn:de:0030-drops-169767
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16976/
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Curticapean, Radu

Determinants from Homomorphisms

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LIPIcs-ESA-2022-38.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{curticapean:LIPIcs.ESA.2022.38,
  author =	{Curticapean, Radu},
  title =	{{Determinants from Homomorphisms}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{38:1--38:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/16976},
  URN =		{urn:nbn:de:0030-drops-169767},
  doi =		{10.4230/LIPIcs.ESA.2022.38},
  annote =	{Keywords: determinant, homomorphisms, matrix trace, Newton identities}
}

Keywords: determinant, homomorphisms, matrix trace, Newton identities
Collection: 30th Annual European Symposium on Algorithms (ESA 2022)
Issue Date: 2022
Date of publication: 01.09.2022

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