Representability of Lyndon-Maddux relation algebras

2017/03/18 by Jeremy F. Alm, Alm, Jeremy F.
Biochemistry, Genetics and Molecular Biology · #03G15 #05D40 #Biological Activity of Diterpenoids and Biflavonoids #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1703.06314

openalex publication_date 2017/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In Alm-Hirsch-Maddux (2016), relation algebras \mathfrakL(q,n) were defined that generalize Roger Lyndon's relation algebras from projective lines, so that \mathfrakL(q,0) is a Lyndon algebra. In that paper, it was shown that if q>2304n²+1, \mathfrakL(q,n) is representable, and if q<2n, \mathfrakL(q,n) is not representable. In the present paper, we reduced this gap by proving that if q≥ n(log n)^1+ε, \mathfrakL(q,n) is representable.

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