TY - JOUR

T1 - Finite and infinite closed-rich words.

AU - Parshina, Olga G.

AU - Puzynina, Svetlana

N1 - DBLP's bibliographic metadata records provided through http://dblp.org/search/publ/api are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.

PY - 2024/2/12

Y1 - 2024/2/12

N2 - A word is called closed if it has a prefix which is also its suffix and there is no internal occurrences of this prefix in the word. In this paper we study words that are rich in closed factors, i.e., which contain the maximal possible number of distinct closed factors. As the main result, we show that for finite words the asymptotics of the maximal number of distinct closed factors in a word of length n is [Formula presented]. For infinite words, we show that there exist words such that each their factor of length n contains a quadratic number of distinct closed factors, with uniformly bounded constant; we call such words infinite closed-rich. We provide several necessary and some sufficient conditions for a word to be infinite closed rich. For example, we show that all linearly recurrent words are closed-rich. We provide a characterization of rich words among Sturmian words. Certain examples we provide involve non-constructive methods.

AB - A word is called closed if it has a prefix which is also its suffix and there is no internal occurrences of this prefix in the word. In this paper we study words that are rich in closed factors, i.e., which contain the maximal possible number of distinct closed factors. As the main result, we show that for finite words the asymptotics of the maximal number of distinct closed factors in a word of length n is [Formula presented]. For infinite words, we show that there exist words such that each their factor of length n contains a quadratic number of distinct closed factors, with uniformly bounded constant; we call such words infinite closed-rich. We provide several necessary and some sufficient conditions for a word to be infinite closed rich. For example, we show that all linearly recurrent words are closed-rich. We provide a characterization of rich words among Sturmian words. Certain examples we provide involve non-constructive methods.

KW - Closed word

KW - Return word

KW - Rich word

UR - https://www.mendeley.com/catalogue/4a6f1e1f-2216-325b-b4b3-4a4d927ce885/

U2 - 10.1016/J.TCS.2023.114315

DO - 10.1016/J.TCS.2023.114315

M3 - Article

VL - 984

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

M1 - 114315

ER -