1Institut für Informatik Christian-Albrechts-Universität zu Kiel Germany 2LIP, ENS de Lyon, France, and Sobolev Institute of Mathematics, Russia 3LIP, CNRS, ENS de Lyon Université de Lyon, France
The electronic journal of combinatorics, Tome 22 (2015) no. 1
In this paper we answer two recent questions from Charlier et al. (2014) and Harju (2013) about self-shuffling words. An infinite word $w$ is called self-shuffling, if $w=\prod_{i=0}^\infty U_iV_i=\prod_{i=0}^\infty U_i=\prod_{i=0}^\infty V_i$ for some finite words $U_i$, $V_i$. Harju recently asked whether square-free self-shuffling words exist. We answer this question affirmatively. Besides that, we build an infinite word such that no word in its shift orbit closure is self-shuffling, answering positively a question of E. Charlier et al.
1
Institut für Informatik
Christian-Albrechts-Universität zu Kiel
Germany
2
LIP, ENS de Lyon, France, and
Sobolev Institute of Mathematics, Russia
3
LIP, CNRS, ENS de Lyon
Université de Lyon, France
@article{10_37236_4825,
author = {Mike M\"uller and Svetlana Puzynina and Micha\"el Rao},
title = {On shuffling of infinite square-free words},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4825},
zbl = {1308.68087},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4825/}
}
TY - JOUR
AU - Mike Müller
AU - Svetlana Puzynina
AU - Michaël Rao
TI - On shuffling of infinite square-free words
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4825/
DO - 10.37236/4825
ID - 10_37236_4825
ER -
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%A Mike Müller
%A Svetlana Puzynina
%A Michaël Rao
%T On shuffling of infinite square-free words
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4825/
%R 10.37236/4825
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Mike Müller; Svetlana Puzynina; Michaël Rao. On shuffling of infinite square-free words. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4825
