Equivalence Classes and Balance Properties of Interleaved Sequences

An interleaved sequence is created from a base sequence and a shift sequence. Interleaved sequences have been studied by several researchers. In this paper we study the relationship between periodicity, reversal and balance proper-ties of the base, shift, and interleaved sequences. We look at equivalence classes of interleaved sequences under the operations of left shift and reversal, and give complete necessary and sufficient conditions to determine the size of the equivalence classes. Additionally, we consider several types of balance. The balance properties we study are more nuanced than previous investigations.