TY - GEN
T1 - Lyndon Words, the Three Squares Lemma, and Primitive Squares
AU - Bannai, Hideo
AU - Mieno, Takuya
AU - Nakashima, Yuto
N1 - Funding Information:
We would like to thank the anonymous reviewers for pointing out and correcting errors in the submitted version of the paper. This work was supported by JSPS KAKENHI Grant Numbers JP20H04141 (HB), JP20J11983 (TM), and JP18K18002 (YN).
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We revisit the so-called “Three Squares Lemma” by Crochemore and Rytter [Algorithmica 1995] and, using arguments based on Lyndon words, derive a more general variant which considers three overlapping squares which do not necessarily share a common prefix. We also give an improved upper bound of on the maximum number of (occurrences of) primitively rooted squares in a string of length n, also using arguments based on Lyndon words. To the best of our knowledge, the only known upper bound was, where is the golden ratio, reported by Fraenkel and Simpson [TCS 1999] obtained via the Three Squares Lemma.
AB - We revisit the so-called “Three Squares Lemma” by Crochemore and Rytter [Algorithmica 1995] and, using arguments based on Lyndon words, derive a more general variant which considers three overlapping squares which do not necessarily share a common prefix. We also give an improved upper bound of on the maximum number of (occurrences of) primitively rooted squares in a string of length n, also using arguments based on Lyndon words. To the best of our knowledge, the only known upper bound was, where is the golden ratio, reported by Fraenkel and Simpson [TCS 1999] obtained via the Three Squares Lemma.
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U2 - 10.1007/978-3-030-59212-7_19
DO - 10.1007/978-3-030-59212-7_19
M3 - Conference contribution
AN - SCOPUS:85092092422
SN - 9783030592110
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 265
EP - 273
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 -