# Integers in number systems with positive and negative quadratic Pisot base

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

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

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topMasáková, 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 -

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