publication . Article . Preprint . 2013

Integers in number systems with positive and negative quadratic Pisot base

Masáková, Zuzana; Vávra, Tomáš;
Open Access
  • Published: 19 Feb 2013 Journal: RAIRO - Theoretical Informatics and Applications, volume 48, pages 341-367 (issn: 0988-3754, eissn: 1290-385X, Copyright policy)
  • Publisher: EDP Sciences
We consider numeration systems with base $\beta$ and $-\beta$, for quadratic Pisot numbers $\beta$ and focus on comparing the combinatorial structure of the sets $\Z_\beta$ and $\Z_{-\beta}$ of numbers with integer expansion in base $\beta$, resp. $-\beta$. Our main result is the comparison of languages of infinite words $u_\beta$ and $u_{-\beta}$ coding the ordering of distances between consecutive $\beta$- and $(-\beta)$-integers. It turns out that for a class of roots $\beta$ of $x^2-mx-m$, the languages coincide, while for other quadratic Pisot numbers the language of $u_\beta$ can be identified only with the language of a morphic image of $u_{-\beta}$. We a...
free text keywords: Software, General Mathematics, Computer Science Applications, Integer, Group structure, Negative base, Combinatorics, Quadratic equation, Mathematics, Mathematics - Number Theory, 11K16, 68R15
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publication . Article . Preprint . 2013

Integers in number systems with positive and negative quadratic Pisot base

Masáková, Zuzana; Vávra, Tomáš;