Upper bound for the number of closed and privileged words

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00345707" target="_blank" >RIV/68407700:21340/20:00345707 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.ipl.2020.105917" target="_blank" >https://doi.org/10.1016/j.ipl.2020.105917</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ipl.2020.105917" target="_blank" >10.1016/j.ipl.2020.105917</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Upper bound for the number of closed and privileged words

Popis výsledku v původním jazyce

A non-empty word w is a border of the word u if |w|<|u| and w is both a prefix and a suffix of u. A word u with the border w is closed if u has exactly two occurrences of w. A word u is privileged if |u|<2 or if u contains a privileged border w that appears exactly twice in u. Peltomäki (2016) presented the following open problem: “Give a nontrivial upper bound for B(n)”, where B(n) denotes the number of privileged words of length n. Let D(n) denote the number of closed words of length n. Let q>1 be the size of the alphabet. We show that there is a positive real constant c such that D(n) <= (c.ln(n).q^n)/(sqrt(n)), where n>1. Privileged words are a subset of closed words, hence we show also an upper bound for the number of privileged words.

Název v anglickém jazyce

Upper bound for the number of closed and privileged words

Popis výsledku anglicky

A non-empty word w is a border of the word u if |w|<|u| and w is both a prefix and a suffix of u. A word u with the border w is closed if u has exactly two occurrences of w. A word u is privileged if |u|<2 or if u contains a privileged border w that appears exactly twice in u. Peltomäki (2016) presented the following open problem: “Give a nontrivial upper bound for B(n)”, where B(n) denotes the number of privileged words of length n. Let D(n) denote the number of closed words of length n. Let q>1 be the size of the alphabet. We show that there is a positive real constant c such that D(n) <= (c.ln(n).q^n)/(sqrt(n)), where n>1. Privileged words are a subset of closed words, hence we show also an upper bound for the number of privileged words.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Information Processing Letters

ISSN

0020-0190

e-ISSN

1872-6119

Svazek periodika

156

Číslo periodika v rámci svazku

April

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

6

Strana od-do

—

Kód UT WoS článku

000514752400006

EID výsledku v databázi Scopus

2-s2.0-85078571909