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Algebra universalis

, 79:54 | Cite as

Representability of Lyndon–Maddux relation algebras

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Part of the following topical collections:
  1. In memory of Bjarni Jónsson

Abstract

In 2016, Alm–Hirsch–Maddux defined relation algebras \(\mathfrak {L}(q,n)\) that generalize Roger Lyndon’s relation algebras from projective lines, so that \(\mathfrak {L}(q,0)\) is a Lyndon algebra. In that paper, it was shown that if \(q>2304n^2+1\), then \(\mathfrak {L}(q,n)\) is representable, and if \(q<2n\), then \(\mathfrak {L}(q,n)\) is not representable. In the present paper, we reduced this gap by proving that if \(q\ge n(\log n)^{1+\varepsilon }\), then \(\mathfrak {L}(q,n)\) is representable.

Keywords

Representable relation algebra Lovász local lemma 

Mathematics Subject Classification

03G15 05D40 

References

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsLamar UniversityBeaumontUSA

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