The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cet article, nous donnons quelques résultats sur les mots primitifs, les mots sans carrés et les langages disjonctifs. Nous montrons cela pour un mot u ∈Σ+, chaque élément de λ(cp(u)) est d-primitive ssi elle est sans carré, où cp(u) est l'ensemble de toutes les permutations cycliques de u, et λ(cp(u)) en est l’ensemble de toutes les racines primitives. Nous montrons ensuite que pmqn est un mot primitif pour chaque n, m ≥1 et mots primitifs p, q, à condition que |p| = |q| et (m, n) ≠ (1, 1). Nous donnons également une condition de disjonction pour une langue.
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Tetsuo MORIYA, "Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages" in IEICE TRANSACTIONS on Information,
vol. E91-D, no. 10, pp. 2514-2516, October 2008, doi: 10.1093/ietisy/e91-d.10.2514.
Abstract: In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u ∈Σ+, every element of λ(cp(u)) is d-primitive iff it is square-free, where cp(u) is the set of all cyclic-permutations of u, and λ(cp(u)) is the set of all primitive roots of it. Next we show that pmqn is a primitive word for every n, m ≥1 and primitive words p, q, under the condition that |p| = |q| and (m, n) ≠ (1, 1). We also give a condition of disjunctiveness for a language.
URL: https://global.ieice.org/en_transactions/information/10.1093/ietisy/e91-d.10.2514/_p
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@ARTICLE{e91-d_10_2514,
author={Tetsuo MORIYA, },
journal={IEICE TRANSACTIONS on Information},
title={Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages},
year={2008},
volume={E91-D},
number={10},
pages={2514-2516},
abstract={In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u ∈Σ+, every element of λ(cp(u)) is d-primitive iff it is square-free, where cp(u) is the set of all cyclic-permutations of u, and λ(cp(u)) is the set of all primitive roots of it. Next we show that pmqn is a primitive word for every n, m ≥1 and primitive words p, q, under the condition that |p| = |q| and (m, n) ≠ (1, 1). We also give a condition of disjunctiveness for a language.},
keywords={},
doi={10.1093/ietisy/e91-d.10.2514},
ISSN={1745-1361},
month={October},}
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TY - JOUR
TI - Some Results on Primitive Words, Square-Free Words, and Disjunctive Languages
T2 - IEICE TRANSACTIONS on Information
SP - 2514
EP - 2516
AU - Tetsuo MORIYA
PY - 2008
DO - 10.1093/ietisy/e91-d.10.2514
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E91-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 2008
AB - In this paper, we give some resuts on primitive words, square-free words and disjunctive languages. We show that for a word u ∈Σ+, every element of λ(cp(u)) is d-primitive iff it is square-free, where cp(u) is the set of all cyclic-permutations of u, and λ(cp(u)) is the set of all primitive roots of it. Next we show that pmqn is a primitive word for every n, m ≥1 and primitive words p, q, under the condition that |p| = |q| and (m, n) ≠ (1, 1). We also give a condition of disjunctiveness for a language.
ER -