### Abstract

Language | English |
---|---|

Pages | 43-50 |

Number of pages | 8 |

Journal | Journal of Automata, Languages and Combinatorics |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 2003 |

### Fingerprint

### Keywords

- Arshon sequence
- morphism
- dragon curve

### Cite this

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*Journal of Automata, Languages and Combinatorics*, vol. 8, no. 1, pp. 43-50.

**There are no iterated morphisms that define the Arshon sequence and the sigma-sequence.** / Kitaev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - There are no iterated morphisms that define the Arshon sequence and the sigma-sequence

AU - Kitaev, Sergey

PY - 2003

Y1 - 2003

N2 - Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.

AB - Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.

KW - Arshon sequence

KW - morphism

KW - dragon curve

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/Arshon.pdf

UR - http://theo.cs.uni-magdeburg.de/cgi-bin/theo/j_bibsearch/jalc/search/j00_i.html

M3 - Article

VL - 8

SP - 43

EP - 50

JO - Journal of Automata, Languages and Combinatorics

T2 - Journal of Automata, Languages and Combinatorics

JF - Journal of Automata, Languages and Combinatorics

SN - 1430-189X

IS - 1

ER -