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.