Exact-m-majority terms
Paolo Lipparini · Mathematica Slovaca · 2024
Abstract We say that an idempotent term t is an exact-m-majority term if t evaluates to a, whenever the element a occurs exactly m times in the arguments of t, and all the other arguments are equal. If m < n and some variety 𝓥 has an n-ary exact-m-majority term, then 𝓥 is congruence modular. For certain values of n and m, for example, n = 5 and m = 3, the existence of an n-ary exact-m-majority term neither implies congruence distributivity, nor congruence permutability.