Avoidable Sets in The Bicycle Inverse Semigroup

Abstract

A subset \(U\) of a set \(S\) with a binary operation is called avoidable if \(S\) can be partitioned into two subsets \(A\) and \(B\) such that no element of \(U\) can be written as a product of two distinct elements of \(A\) or as the product of two distinct elements of \(B\). The avoidable sets of the bicyclic inverse semigroup are classified.