Geodesic
SUBBLOCK OCCURRENCES IN SIGNED DIGIT REPRESENTATIONS
Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 427-440

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DOI

Signed digit representations with base $q$ and digits $-\frac q2,\dots,\frac q2$ (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 $0,\dots,n-1$ turns out to be const $\cdot\log_qn+\delta(\log_qn)+\smallOh(1)$, 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.
DOI : 10.1017/S0017089503001368
Mots-clés : Primary: 11K16, Secondary: 11A63, 11M41 
GRABNER, PETER J.; HEUBERGER, CLEMENS; PRODINGER, HELMUT. SUBBLOCK OCCURRENCES IN SIGNED DIGIT REPRESENTATIONS. Glasgow mathematical journal, Tome 45 (2003) no. 3, pp. 427-440. doi: 10.1017/S0017089503001368
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     title = {SUBBLOCK {OCCURRENCES} {IN} {SIGNED} {DIGIT} {REPRESENTATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {427--440},
     year = {2003},
     volume = {45},
     number = {3},
     doi = {10.1017/S0017089503001368},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089503001368/}
}
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