Relative lengths of Maltsev conditions (Q6553452)

It is well known that congruence distributive varieties are characterized by a sequence of Jónsson terms [\textit{B. Jonsson}, Math. Scand. 21, 110--121 (1967; Zbl 0167.28401)], respectively, congruence modular varieties are determined by a sequence of Day terms [\textit{A. Day}, Can. Math. Bull. 12, 167--173 (1969; Zbl 0181.02302)]. It is natural to ask about the relationship between both types of terms. Day showed [loc. cit.] that a variety with \(n\) Jónsson terms has \(2n-1\) Day terms and wondered if the result is optimal. The author of the paper shows that it is true in locally finite varieties for \(n\) being even. The author also considers other terms, such as Gumm, alivin, directed, or reversed terms. The proofs are based on ``constructing appropriate counterexamples by induction. In each case, induction at step \(n\) uses the counterexample constructed for \(n-2\) in the parallel theorem'' [from the page 9].