Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00221153" target="_blank" >RIV/68407700:21340/15:00221153 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21240/15:00221153

Výsledek na webu

<a href="http://dx.doi.org/10.5802/jtnb.922" target="_blank" >http://dx.doi.org/10.5802/jtnb.922</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5802/jtnb.922" target="_blank" >10.5802/jtnb.922</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems

Popis výsledku v původním jazyce

In this paper we study the expansions of real numbers in positive and negative real base as introduced by Rényi, and Ito & Sadahiro, respectively. In particular, we compare the sets ? ? + and ? -? of nonnegative ?-integers and (-?)-integers. We describeall bases (??) for which ? ? + and ? -? can be coded by infinite words which are fixed points of conjugated morphisms, and consequently have the same language. Moreover, we prove that this happens precisely for ? with another interesting property, namelythat any linear combination of non-negative powers of the base -? with coefficients in {0,1,...,[?]} is a (-?)-integer, although the corresponding sequence of digits is forbidden as a (-?)-expansion.

Název v anglickém jazyce

Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems

Popis výsledku anglicky

In this paper we study the expansions of real numbers in positive and negative real base as introduced by Rényi, and Ito & Sadahiro, respectively. In particular, we compare the sets ? ? + and ? -? of nonnegative ?-integers and (-?)-integers. We describeall bases (??) for which ? ? + and ? -? can be coded by infinite words which are fixed points of conjugated morphisms, and consequently have the same language. Moreover, we prove that this happens precisely for ? with another interesting property, namelythat any linear combination of non-negative powers of the base -? with coefficients in {0,1,...,[?]} is a (-?)-integer, although the corresponding sequence of digits is forbidden as a (-?)-expansion.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/GA13-03538S" target="_blank" >GA13-03538S: Algoritmy, dynamika a geometrie numeračních systémů</a><br>

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

J. Theor. Nombres Bordeaux

ISSN

1246-7405

e-ISSN

—

Svazek periodika

27

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

FR - Francouzská republika

Počet stran výsledku

24

Strana od-do

745-768

Kód UT WoS článku

000369204300007

EID výsledku v databázi Scopus

2-s2.0-84947590631