SUBBLOCK OCCURRENCES IN SIGNED DIGIT REPRESENTATIONS

Signed digit representations with base q and digits –q/2,…,q/2 (and uniqueness being enforced by applying a special rule which decides whether -q/2 or q/2 should be taken) are considered with respect to counting the occurrences of a given (contiguous) subblock of length r. The average number of occurrences amongst the numbers 0,…,n-1 turns out to be const . log_qn+ (delta)(log_qn)+(Oh)(1), with a constant and a periodic function of period one depending on the given subblock; they are explicitly described. Furthermore, we use probabilistic techniques to prove a central limit theorem for the number of occurrences of a given subblock.