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On the Existence of Minimal beta-Powers. / Shur, Arseny M.
Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings : book. ed. / Y. Gao. Vol. 6224 BERLIN: Springer Verlag, 2010. p. 411-422 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Shur, AM 2010, On the Existence of Minimal beta-Powers. in Y Gao (ed.), Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings : book. vol. 6224, Lecture Notes in Computer Science, Springer Verlag, BERLIN, pp. 411-422. https://doi.org/10.1007/978-3-642-14455-4_37

APA

Shur, A. M. (2010). On the Existence of Minimal beta-Powers. In Y. Gao (Ed.), Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings : book (Vol. 6224, pp. 411-422). (Lecture Notes in Computer Science). Springer Verlag. https://doi.org/10.1007/978-3-642-14455-4_37

Vancouver

Shur AM. On the Existence of Minimal beta-Powers. In Gao Y, editor, Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings : book. Vol. 6224. BERLIN: Springer Verlag. 2010. p. 411-422. (Lecture Notes in Computer Science). doi: 10.1007/978-3-642-14455-4_37

Author

Shur, Arseny M. / On the Existence of Minimal beta-Powers. Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings : book. editor / Y. Gao. Vol. 6224 BERLIN : Springer Verlag, 2010. pp. 411-422 (Lecture Notes in Computer Science).

BibTeX

@inproceedings{44816c2a64da4b4a8d469af4a52dc2e9,
title = "On the Existence of Minimal beta-Powers",
abstract = "If all proper factors of a word u are beta-power-free while u itself is not, then u is a minimal beta-power. We consider the following general problem: for which numbers k, beta, and p there exists a k-ary minimal beta-power of period p? For the case beta >= 2 we completely solve this problem. If the number beta < 2 is relatively {"}big{"} w.r.t. k, we show that any number p can be the period of a minimal beta-power. Finally, for {"}small{"} beta we describe some sets of forbidden periods and provide a numerical evidence that for k >= 9 these sets are almost exhaustive.",
author = "Shur, {Arseny M.}",
year = "2010",
doi = "10.1007/978-3-642-14455-4_37",
language = "English",
isbn = "978-3-642-14454-7",
volume = "6224",
series = "Lecture Notes in Computer Science",
publisher = "Springer Verlag",
pages = "411--422",
editor = "Y. Gao",
booktitle = "Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings",
address = "Germany",

}

RIS

TY - GEN

T1 - On the Existence of Minimal beta-Powers

AU - Shur, Arseny M.

PY - 2010

Y1 - 2010

N2 - If all proper factors of a word u are beta-power-free while u itself is not, then u is a minimal beta-power. We consider the following general problem: for which numbers k, beta, and p there exists a k-ary minimal beta-power of period p? For the case beta >= 2 we completely solve this problem. If the number beta < 2 is relatively "big" w.r.t. k, we show that any number p can be the period of a minimal beta-power. Finally, for "small" beta we describe some sets of forbidden periods and provide a numerical evidence that for k >= 9 these sets are almost exhaustive.

AB - If all proper factors of a word u are beta-power-free while u itself is not, then u is a minimal beta-power. We consider the following general problem: for which numbers k, beta, and p there exists a k-ary minimal beta-power of period p? For the case beta >= 2 we completely solve this problem. If the number beta < 2 is relatively "big" w.r.t. k, we show that any number p can be the period of a minimal beta-power. Finally, for "small" beta we describe some sets of forbidden periods and provide a numerical evidence that for k >= 9 these sets are almost exhaustive.

UR - https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=tsmetrics&SrcApp=tsm_test&DestApp=WOS_CPL&DestLinkType=FullRecord&KeyUT=000286402700037

U2 - 10.1007/978-3-642-14455-4_37

DO - 10.1007/978-3-642-14455-4_37

M3 - Conference contribution

SN - 978-3-642-14454-7

VL - 6224

T3 - Lecture Notes in Computer Science

SP - 411

EP - 422

BT - Developments in Language Theory, 14th International Conference, DLT 2010, Proceedings

A2 - Gao, Y.

PB - Springer Verlag

CY - BERLIN

ER -

ID: 37896316