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.
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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 -