On some properties of doubly-periodic words
- Volume: 8, Issue: 1, page 39-47
- ISSN: 1120-6330
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topBaiocchi, Claudio. "On some properties of doubly-periodic words." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 8.1 (1997): 39-47. <http://eudml.org/doc/244229>.
@article{Baiocchi1997,
abstract = {We study the functional equation: \( (1) \, ABC = CDA \) where \(A, B, C\) and \(D\) are words over an alphabet \( \mathcal\{A\} \). In particular we prove a «structure result» for the inner factors \(B, D\): for suitably chosen words \(X, Y, Z\) one has: \( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\). It is a generalization of the Lyndon-Schützenberger's Theorem (see [7]): if in (1) \(A\) or \(C\) is empty, formula (2) holds true with one among \(X, Y, Z\) which can be chosen empty.},
author = {Baiocchi, Claudio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Words; Periodicity; Palindromy; doubly-periodic words},
language = {eng},
month = {4},
number = {1},
pages = {39-47},
publisher = {Accademia Nazionale dei Lincei},
title = {On some properties of doubly-periodic words},
url = {http://eudml.org/doc/244229},
volume = {8},
year = {1997},
}
TY - JOUR
AU - Baiocchi, Claudio
TI - On some properties of doubly-periodic words
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1997/4//
PB - Accademia Nazionale dei Lincei
VL - 8
IS - 1
SP - 39
EP - 47
AB - We study the functional equation: \( (1) \, ABC = CDA \) where \(A, B, C\) and \(D\) are words over an alphabet \( \mathcal{A} \). In particular we prove a «structure result» for the inner factors \(B, D\): for suitably chosen words \(X, Y, Z\) one has: \( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\)\( (2) \, B =XYZ\), \(D = ZYX\). It is a generalization of the Lyndon-Schützenberger's Theorem (see [7]): if in (1) \(A\) or \(C\) is empty, formula (2) holds true with one among \(X, Y, Z\) which can be chosen empty.
LA - eng
KW - Words; Periodicity; Palindromy; doubly-periodic words
UR - http://eudml.org/doc/244229
ER -
References
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- DE LUCA, A., Sturmian words: Structure, Combinatorics, and their Arithmetics. Theoretical Computer Science, special issue on Formal Language, to appear. Zbl0911.68098
- DE LUCA, A. - MIGNOSI, F., Some combinatorial properties of sturmian words. Theoretical Computer Science, 136, 1994, 361-385. Zbl0874.68245MR1311214DOI10.1016/0304-3975(94)00035-H
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- LOTHAIRE, M., Combinatorics on Words. Addison-Wesley, Reading, MA, 1983. Zbl0514.20045MR675953
- LYNDON, R. C. - SCHÜTZENBERGER, M. P., On the equation in a free group. Michigan Math. J., 9, 1962, 289-298. Zbl0106.02204MR162838
- PERDERSEN, A., Solution of Problem E 3156. The American Mathematical Monthly, 95, 1988, 954-955.
- ROBINSON, P. M., Problem E 3156. The American Mathematical Monthly, 93, 1986, 482.
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