Mitschke's Theorem is sharp

Abstract

A. Mitschke showed that a variety with an $m$-ary near-unanimity term has Jónsson terms $t_0,\dots ,t_{2m-4}$ witnessing congruence distributivity. We show that Mitschke's result is sharp. We also evaluate the best possible number of Day terms witnessing congruence modularity. More generally, we characterize exactly the best bounds for many congruence identities satisfied by varieties with an $m$-ary near-unanimity term.

v2 a few improvements, some simplifications, some exemplifications v3 minor fixes, a few improvements, some more notions introduced

References in corpus (3)

• Relation identities in 3-distributive varieties
• Mitschke's Theorem is sharp
• The distributivity spectrum of Baker's variety

Cited by in corpus (3)

• Mitschke's Theorem is sharp
• Exact-$m$-majority terms
• Day's Theorem is sharp for $n$ even