Learning seminar on Finite Relational Structures

Carrie Knoll, Department of Pure Mathematics,  University of Waterloo

“Idempotent operations in reflexive digraphs”

Every projection map is idempotent, but the converse is not necessarily true. In a general structure A, it is possible that the only binary idempotent operations on A are the binary projection maps, but we can find a 3-ary idempotent operation that is not a projection. This cannot happen for finite reflexive digraphs. We will show that if there is some n ≥ 2 such that every n-ary idempotent operation is a projection, then the same holds for all n ≥ 2.