Finite representations for two small relation algebras

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.