  In this note, we consider the problem of counting and verifying abelian
border arrays of binary words. We show that the number of valid abelian border
arrays of length \(n\) is \(2^{n-1}\). We also show that verifying whether a
given array is the abelian border array of some binary word reduces to
computing the abelian border array of a specific binary word. Thus, assuming
the word-RAM model, we present an \(O\left(\frac{n^2}{\log^2n}\right)\) time
algorithm for the abelian border array verification problem.
