Palindromic Length of Words with Many Periodic Palindromes

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Palindromic Length of Words with Many Periodic Palindromes
Original language description
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.
Czech name
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Czech description
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Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
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
Number of pages
13
Pages from-to
167-179
Publisher name
Springer, Cham
Place of publication
—
Event location
Vienna
Event date
Aug 24, 2020
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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