Families of periodic Jacobi-Perron algorithms for all period lengths

For all integers m >= n >= 2, we exhibit infinite families of purely periodic Jacobi-Perron Algorithm (JPA) expansions of dimension n with period length equal to m along with the associated Hasse-Bernstein units. Some observations on the units of Levesque-Rhin as well as the periodicity of the JPA expansion of (m(1/3), m(2/3)) are also made. (C) 2016 Published by Elsevier Inc.