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We prove that the subsets of that are S-recognizable for all abstract numeration systems S are exactly the 1-recognizable sets. This generalizes a result of Lecomte and Rigo in the one-dimensional setting.
@article{ITA_2012__46_1_51_0,
author = {Charlier, \'Emilie and Lacroix, Anne and Rampersad, Narad},
title = {Multi-dimensional sets recognizable in all abstract numeration systems},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {51--65},
publisher = {EDP-Sciences},
volume = {46},
number = {1},
year = {2012},
doi = {10.1051/ita/2011112},
mrnumber = {2904960},
zbl = {1254.68132},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011112/}
}
TY - JOUR AU - Charlier, Émilie AU - Lacroix, Anne AU - Rampersad, Narad TI - Multi-dimensional sets recognizable in all abstract numeration systems JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2012 SP - 51 EP - 65 VL - 46 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011112/ DO - 10.1051/ita/2011112 LA - en ID - ITA_2012__46_1_51_0 ER -
%0 Journal Article %A Charlier, Émilie %A Lacroix, Anne %A Rampersad, Narad %T Multi-dimensional sets recognizable in all abstract numeration systems %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2012 %P 51-65 %V 46 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011112/ %R 10.1051/ita/2011112 %G en %F ITA_2012__46_1_51_0
Charlier, Émilie; Lacroix, Anne; Rampersad, Narad. Multi-dimensional sets recognizable in all abstract numeration systems. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 1, pp. 51-65. doi: 10.1051/ita/2011112
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