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Algebra universalis

, 79:87 | Cite as

Finite representations for two small relation algebras

  • Jeremy F. Alm
  • Roger D. Maddux
Article
  • 5 Downloads
Part of the following topical collections:
  1. In memory of Bjarni Jónsson

Abstract

In this note, we prove that two different finite relation algebras are representable over finite sets. We give an explicit group representation of \(52_{65}\) over \( (\mathbb {Z}/2\mathbb {Z})^{10}\). We also give a representation of \(59_{65}\) over \(\mathbb {Z}/113\mathbb {Z}\) using a technique due to Comer.

Keywords

Relation algebra Finite representation 

Mathematics Subject Classification

03G15 11B13 

References

  1. 1.
    Alm, J.F., Ylvisaker, A.: A fast coset-translation algorithm for computing the cycle structure of Comer relation algebras over \({\mathbb{Z}}/p{\mathbb{Z}}\) (2017). arXiv:1708.04974
  2. 2.
    Comer, S.D.: Color schemes forbidding monochrome triangles. In: Proceedings of the Fourteenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Boca Raton, Fla., 1983), vol. 39, pp. 231–236 (1983)Google Scholar
  3. 3.
    Maddux, R.D.: Relation Algebras. Studies in Logic and the Foundations of Mathematics, vol. 150. Elsevier B. V., Amsterdam (2006)zbMATHGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsLamar UniversityBeaumontUSA
  2. 2.Department of MathematicsIowa State UniversityAmesUSA

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