TY - GEN
T1 - On Repetitiveness Measures of Thue-Morse Words
AU - Kutsukake, Kanaru
AU - Matsumoto, Takuya
AU - Nakashima, Yuto
AU - Inenaga, Shunsuke
AU - Bannai, Hideo
AU - Takeda, Masayuki
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP18K18002 (YN), JP17H01697 (SI), JP16H02783, JP20H04141 (HB), JP18H04098 (MT), and JST PRESTO Grant Number JPMJPR1922 (SI).
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We show that the size of the smallest string attractor of the n-th Thue-Morse word is 4 for any, disproving the conjecture by Mantaci et al. [ICTCS 2019] that it is n. We also show that for, where is the maximum over all, the number of distinct substrings of length k in w divided by k, which is a measure of repetitiveness recently studied by Kociumaka et al. [LATIN 2020]. Furthermore, we show that the number of factors in the self-referencing Lempel-Ziv factorization of is exactly 2n.
AB - We show that the size of the smallest string attractor of the n-th Thue-Morse word is 4 for any, disproving the conjecture by Mantaci et al. [ICTCS 2019] that it is n. We also show that for, where is the maximum over all, the number of distinct substrings of length k in w divided by k, which is a measure of repetitiveness recently studied by Kociumaka et al. [LATIN 2020]. Furthermore, we show that the number of factors in the self-referencing Lempel-Ziv factorization of is exactly 2n.
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U2 - 10.1007/978-3-030-59212-7_15
DO - 10.1007/978-3-030-59212-7_15
M3 - Conference contribution
AN - SCOPUS:85092092768
SN - 9783030592110
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 213
EP - 220
BT - String Processing and Information Retrieval - 27th International Symposium, SPIRE 2020, Proceedings
A2 - Boucher, Christina
A2 - Thankachan, Sharma V.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Symposium on String Processing and Information Retrieval, SPIRE 2020
Y2 - 13 October 2020 through 15 October 2020
ER -