Palindromic factorization of rich words

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00361403" target="_blank" >RIV/68407700:21340/22:00361403 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.dam.2022.03.030" target="_blank" >https://doi.org/10.1016/j.dam.2022.03.030</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2022.03.030" target="_blank" >10.1016/j.dam.2022.03.030</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Palindromic factorization of rich words

Popis výsledku v původním jazyce

A finite word w is called rich if it contains |w|+1 distinct palindromic factors including the empty word. For every finite rich word w there are distinct nonempty palindromes w(1), w(2), ..., w(p) such that w = w(p)w(p-1) ... w(1) and w(i) is the longest palindromic suffix of w(p)w(p-1) ... w(i), where 1 <= i <= p. This palindromic factorization is called UPS-factorization. Let luf(w) = p be the length of UPS-factorization of w. In 2017, it was proved that there is a constant c such that if w is a finite rich word and n=|w| then luf(w) <= cn/(ln n). We improve this result as follows: There are positive constants m, k such that if w is a finite rich word and n=|w| then luf(w) <= m*n/exp(k*root(ln n)). The constants c, m, k depend on the size of the alphabet.

Název v anglickém jazyce

Palindromic factorization of rich words

Popis výsledku anglicky

A finite word w is called rich if it contains |w|+1 distinct palindromic factors including the empty word. For every finite rich word w there are distinct nonempty palindromes w(1), w(2), ..., w(p) such that w = w(p)w(p-1) ... w(1) and w(i) is the longest palindromic suffix of w(p)w(p-1) ... w(i), where 1 <= i <= p. This palindromic factorization is called UPS-factorization. Let luf(w) = p be the length of UPS-factorization of w. In 2017, it was proved that there is a constant c such that if w is a finite rich word and n=|w| then luf(w) <= cn/(ln n). We improve this result as follows: There are positive constants m, k such that if w is a finite rich word and n=|w| then luf(w) <= m*n/exp(k*root(ln n)). The constants c, m, k depend on the size of the alphabet.

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

2022

Kód důvěrnosti údajů

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

Název periodika

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

1872-6771

Svazek periodika

316

Číslo periodika v rámci svazku

July

Stát vydavatele periodika

AT - Rakouská republika

Počet stran výsledku

8

Strana od-do

95-102

Kód UT WoS článku

000806207100002

EID výsledku v databázi Scopus

2-s2.0-85130066388