Arguesian lattices which are not linear
Mark D. Haiman · Bulletin of the American Mathematical Society · 1987
A linear lattice is one representable by commuting equivalence relations.We construct a sequence of finite lattices A n (n > 3) with the properties: (i) A n is not linear, (ii) every proper sublattice of A n is linear, and (iii) any set of generators for A n has at least n elements.In particular, A n is then Arguesian for n > 7.This settles a question raised in 1953 by Jónsson.