Abstract
We obtain representations for relation algebras corresponding to certain edge colourings of complete graphs. Suitable colourings are obtained for the number of colours n up to 120, with two exceptions: n = 8 and n = 13. For n > 7, it was not known whether representations exist.
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Alm, J., Manske, J.: Sum-free cyclic multi-bases and constructions of Ramsey algebras (2013). ArXiv: 1307.0889v2
Comer S.: Color schemes forbidding monochrome triangles. Congr. Numer. 39, 231–236 (1983)
Fettes, S., Kramer, R., Radziszowski, S.: An upper bound of 62 on the classical Ramsey number R(3, 3, 3, 3). Ars Combin. LXXII, 41–63 (2004)
Greenwood R., Gleason A.: Combinatorial relations and chromatic graphs. Canad. J. Math. 7, 1–7 (1965)
Hirsch R., Hodkinson I.: Representability is not decidable for finite relation algebras. Trans. Amer. Math. Soc. 353, 1403–1425 (2001)
Hirsch, R., Hodkinson, I.: Relation algebras by games. North-Holland. Elsevier Science, Amsterdam (2002)
Jónsson B.: Varieties of relation algebras. Algebra Universalis 15, 273–298 (1982)
Jónsson B., Tarski A.: Boolean algebras with operators II. Amer. J. Math. 74, 127–162 (1952)
Maddux, R.: Relation algebras. North-Holland. Elsevier Science, Amsterdam (2006)
Maddux, R.: Do Ramsey algebras exist? Talk at AMS Sectional Meeting, March 18–20, 2011, University of Iowa, Iowa City
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Presented by B. Davey.
Dedicated to Brian Davey on the occasion of his 65th birthday
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Kowalski, T. Representability of Ramsey Relation Algebras. Algebra Univers. 74, 265–275 (2015). https://doi.org/10.1007/s00012-015-0353-0
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DOI: https://doi.org/10.1007/s00012-015-0353-0