Skip to main content
×
Home

Integers in number systems with positive and negative quadratic Pisot base

  • Z. Masáková (a1) and T. Vávra (a1)
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 Zβ of numbers with integer expansion in base β, resp. − β. Our main result is the comparison of languages of infinite words uβ and uβ coding the ordering of distances between consecutive β- and (− β)-integers. It turns out that for a class of roots β of x2mxm, 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 uβ. We also study the group structure of (− β)-integers.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

RAIRO - Theoretical Informatics and Applications
  • ISSN: 0988-3754
  • EISSN: 1290-385X
  • URL: /core/journals/rairo-theoretical-informatics-and-applications
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 1 *
Loading metrics...

Abstract views

Total abstract views: 17 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th November 2017. This data will be updated every 24 hours.