Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • Integers in number systems with positive and negative quadraticPisot base

  • Z. Masáková, T. Vávra
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 48 / Issue 3 / July 2014
    Published online by Cambridge University Press:
    13 June 2014, pp. 341-367
    Print publication:
    July 2014

  • We consider numeration systems with base β and −β, for quadratic Pisot numbers β and focus on comparingthe combinatorial structure of the sets Zβ and Z− β of numberswith integer expansion in base β, resp. − β. Our main result is the comparison of languagesof infinite words uβ andu−β coding the ordering of distances betweenconsecutive β- and (−β)-integers. It turns out that for a class of rootsβ ofx2 −mx − m, the languages coincide,while for other quadratic Pisot numbers the language of uβ can be identified onlywith the language of a morphic image of u− β. We also study thegroup structure of (−β)-integers.