Integers in number systems with positive and negative quadratic Pisot base

Z. Masáková; T. Vávra

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2014)

  • Volume: 48, Issue: 3, page 341-367
  • ISSN: 0988-3754

Abstract

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We consider numeration systems with base β and − β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z− β of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and u− β coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2 − mx − m, the languages coincide, while for other quadratic Pisot numbers the language of uβ can be identified only with the language of a morphic image of u− β. We also study the group structure of (− β)-integers.

How to cite

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Masáková, Z., and Vávra, T.. "Integers in number systems with positive and negative quadratic Pisot base." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 48.3 (2014): 341-367. <http://eudml.org/doc/273038>.

@article{Masáková2014,
abstract = {We consider numeration systems with base β and − β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z− β of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and u− β coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2 − mx − m, the languages coincide, while for other quadratic Pisot numbers the language of uβ can be identified only with the language of a morphic image of u− β. We also study the group structure of (− β)-integers.},
author = {Masáková, Z., Vávra, T.},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {quadratic Pisot numbers; beta-integers; negative base},
language = {eng},
number = {3},
pages = {341-367},
publisher = {EDP-Sciences},
title = {Integers in number systems with positive and negative quadratic Pisot base},
url = {http://eudml.org/doc/273038},
volume = {48},
year = {2014},
}

TY - JOUR
AU - Masáková, Z.
AU - Vávra, T.
TI - Integers in number systems with positive and negative quadratic Pisot base
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2014
PB - EDP-Sciences
VL - 48
IS - 3
SP - 341
EP - 367
AB - We consider numeration systems with base β and − β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z− β of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and u− β coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2 − mx − m, the languages coincide, while for other quadratic Pisot numbers the language of uβ can be identified only with the language of a morphic image of u− β. We also study the group structure of (− β)-integers.
LA - eng
KW - quadratic Pisot numbers; beta-integers; negative base
UR - http://eudml.org/doc/273038
ER -

References

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