Let be an integer-valued polynomial taking only positive values and let be a fixed positive integer. The aim of this short note is to show, by elementary means, that for any sufficiently large integer there exists such that contains exactly occurrences of the block of size in its digital expansion in base . The method of proof allows to give a lower estimate on the number of “0” resp. “1” symbols in polynomial extractions in the Rudin–Shapiro sequence.
Accepté le :
DOI : 10.1051/ita/2016009
Mots-clés : Rudin–Shapiro sequence, automatic sequences, polynomials
@article{ITA_2016__50_1_93_0,
author = {Stoll, Thomas},
title = {On digital blocks of polynomial values and extractions in the {Rudin{\textendash}Shapiro} sequence},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {93--99},
publisher = {EDP-Sciences},
volume = {50},
number = {1},
year = {2016},
doi = {10.1051/ita/2016009},
zbl = {1419.11014},
mrnumber = {3518161},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/ita/2016009/}
}
TY - JOUR AU - Stoll, Thomas TI - On digital blocks of polynomial values and extractions in the Rudin–Shapiro sequence JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2016 SP - 93 EP - 99 VL - 50 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita/2016009/ DO - 10.1051/ita/2016009 LA - en ID - ITA_2016__50_1_93_0 ER -
%0 Journal Article %A Stoll, Thomas %T On digital blocks of polynomial values and extractions in the Rudin–Shapiro sequence %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2016 %P 93-99 %V 50 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita/2016009/ %R 10.1051/ita/2016009 %G en %F ITA_2016__50_1_93_0
Stoll, Thomas. On digital blocks of polynomial values and extractions in the Rudin–Shapiro sequence. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Special issue dedicated to the 15th "Journées Montoises d'Informatique Théorique", Tome 50 (2016) no. 1, pp. 93-99. doi : 10.1051/ita/2016009. http://archive.numdam.org/articles/10.1051/ita/2016009/
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