Palindromic Length of Words with Many Periodic Palindromes

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00345711" target="_blank" >RIV/68407700:21340/20:00345711 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-030-62536-8_14" target="_blank" >https://doi.org/10.1007/978-3-030-62536-8_14</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-030-62536-8_14" target="_blank" >10.1007/978-3-030-62536-8_14</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Palindromic Length of Words with Many Periodic Palindromes

Popis výsledku v původním jazyce

The palindromic length PL(v) of a finite word v is the minimal number of palindromes whose concatenation is equal to v. In 2013, Frid, Puzynina, and Zamboni conjectured that: If w is an infinite word and k is an integer such that PL(u)<=k for every factor u of w then w is ultimately periodic. Suppose that w is an infinite word and k is an integer such PL(u)<=k for every factor u of w. Let Ω(w,k) be the set of all factors u of w that have more than sqrt[k](k^{-1}|u|) palindromic prefixes. We show that Ω(w,k) is an infinite set and we show that for each positive integer j there are palindromes a, b and a word u in Ω(w,k) such that (ab)^j is a factor of u and b is nonempty. Note that (ab)^j is a periodic word and (ab)^ia is a palindrome for each i<=j. These results justify the following question: What is the palindromic length of a concatenation of a suffix of b and a periodic word (ab)^j with “many” periodic palindromes? It is known that if u, v are nonempty words then |PL(uv)-PL(u)|<=PL(v). The main result of our article shows that if a, b are palindromes, b is nonempty, u is a nonempty suffix of b, |ab| is the minimal period of aba, and j is a positive integer with j>=3PL(u) then PL(u(ab)^j)-PL(u)>=0.

Název v anglickém jazyce

Palindromic Length of Words with Many Periodic Palindromes

Popis výsledku anglicky

The palindromic length PL(v) of a finite word v is the minimal number of palindromes whose concatenation is equal to v. In 2013, Frid, Puzynina, and Zamboni conjectured that: If w is an infinite word and k is an integer such that PL(u)<=k for every factor u of w then w is ultimately periodic. Suppose that w is an infinite word and k is an integer such PL(u)<=k for every factor u of w. Let Ω(w,k) be the set of all factors u of w that have more than sqrt[k](k^{-1}|u|) palindromic prefixes. We show that Ω(w,k) is an infinite set and we show that for each positive integer j there are palindromes a, b and a word u in Ω(w,k) such that (ab)^j is a factor of u and b is nonempty. Note that (ab)^j is a periodic word and (ab)^ia is a palindrome for each i<=j. These results justify the following question: What is the palindromic length of a concatenation of a suffix of b and a periodic word (ab)^j with “many” periodic palindromes? It is known that if u, v are nonempty words then |PL(uv)-PL(u)|<=PL(v). The main result of our article shows that if a, b are palindromes, b is nonempty, u is a nonempty suffix of b, |ab| is the minimal period of aba, and j is a positive integer with j>=3PL(u) then PL(u(ab)^j)-PL(u)>=0.

Druh

D - Stať ve sborníku

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 statě ve sborníku

22nd International Conference, DCFS 2020, Vienna, Austria, August 24–26, 2020, Proceedings

ISBN

978-3-030-62535-1

ISSN

0302-9743

e-ISSN

1611-3349

Počet stran výsledku

13

Strana od-do

167-179

Název nakladatele

Springer, Cham

Místo vydání

—

Místo konání akce

Vienna

Datum konání akce

24. 8. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—