Subblock Occurrences in Signed Digit Representations
نویسندگان
چکیده
Abstract. 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 q n + δ(log q n) + o(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.
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