About: Integers in number systems with positive and negative quadratic Pisot base     Goto   Sponge   NotDistinct   Permalink

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  • We consider numeration systems with base beta and -beta for quadratic Pisot numbers 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 innite 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 of x2 - mx - m, the languages coincide, while for other quadratic Pisot numbers the language of u_beta can be identied only with the language of a morphic image of u_(-beta). We also study the group structure of (-beta)-integers.
  • We consider numeration systems with base beta and -beta for quadratic Pisot numbers 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 innite 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 of x2 - mx - m, the languages coincide, while for other quadratic Pisot numbers the language of u_beta can be identied only with the language of a morphic image of u_(-beta). We also study the group structure of (-beta)-integers. (en)
Title
  • Integers in number systems with positive and negative quadratic Pisot base
  • Integers in number systems with positive and negative quadratic Pisot base (en)
skos:prefLabel
  • Integers in number systems with positive and negative quadratic Pisot base
  • Integers in number systems with positive and negative quadratic Pisot base (en)
skos:notation
  • RIV/68407700:21340/14:00208925!RIV15-MSM-21340___
http://linked.open...avai/riv/aktivita
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  • P(GA13-03538S), S
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  • 3
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  • 22124
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  • RIV/68407700:21340/14:00208925
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  • Pisot numbers; non-standard numeration systems; negative base (en)
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  • FR - Francouzská republika
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  • [642ACD7C502F]
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  • RAIRO - Theoretical Informatics and Applications
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  • 48
http://linked.open...iv/tvurceVysledku
  • Masáková, Zuzana
  • Vávra, Tomáš
http://linked.open...ain/vavai/riv/wos
  • 000339168900007
issn
  • 0988-3754
number of pages
http://bibframe.org/vocab/doi
  • 10.1051/ita/2014013
http://localhost/t...ganizacniJednotka
  • 21340
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