Dumont-Thomas Complement Numeration Systems for Z

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00379531" target="_blank" >RIV/68407700:21340/24:00379531 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.5281/zenodo.14340125" target="_blank" >https://doi.org/10.5281/zenodo.14340125</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.5281/zenodo.14340125" target="_blank" >10.5281/zenodo.14340125</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Dumont-Thomas Complement Numeration Systems for Z

Popis výsledku v původním jazyce

We extend the well-known Dumont-Thomas numeration systems to Z using an approach inspired by the two’s complement numeration system. Integers in Z are canonically represented by a finite word (starting with 0 when nonnegative and with 1 when negative). The systems are based on two-sided periodic points of substitutions as opposed to the right-sided fixed points. For every periodic point of a substitution, we construct an automaton which returns the letter at position n element Z of the periodic point when fed with the representation of n in the corresponding numeration system. The numeration system naturally extends to Zd. We give an equivalent characterization of the numeration system in terms of a total order on a regular language. Lastly, using particular periodic points, we recover the well-known two’s complement numeration system and the Fibonacci analogue of the two’s complement numeration system.

Název v anglickém jazyce

Dumont-Thomas Complement Numeration Systems for Z

Popis výsledku anglicky

We extend the well-known Dumont-Thomas numeration systems to Z using an approach inspired by the two’s complement numeration system. Integers in Z are canonically represented by a finite word (starting with 0 when nonnegative and with 1 when negative). The systems are based on two-sided periodic points of substitutions as opposed to the right-sided fixed points. For every periodic point of a substitution, we construct an automaton which returns the letter at position n element Z of the periodic point when fed with the representation of n in the corresponding numeration system. The numeration system naturally extends to Zd. We give an equivalent characterization of the numeration system in terms of a total order on a regular language. Lastly, using particular periodic points, we recover the well-known two’s complement numeration system and the Fibonacci analogue of the two’s complement numeration system.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Integers: Electronic Journal of Combinatorial Number Theory

ISSN

1553-1732

e-ISSN

1553-1732

Svazek periodika

24

Číslo periodika v rámci svazku

A112

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

—

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-86000505543