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.
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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
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)
Maddux, R.D.: Relation Algebras. Studies in Logic and the Foundations of Mathematics, vol. 150. Elsevier B. V., Amsterdam (2006)
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Presented by J. B. Nation.
This article is dedicated to the memory of Bjarni Jonsson.
This article is part of the topical collection “In memory of Bjarni Jónsson” edited by J. B. Nation.
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Alm, J.F., Maddux, R.D. Finite representations for two small relation algebras. Algebra Univers. 79, 87 (2018). https://doi.org/10.1007/s00012-018-0570-4
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DOI: https://doi.org/10.1007/s00012-018-0570-4