Research output: Contribution to journal › Article › peer-review
Aperiodic two-dimensional words of small abelian complexity. / Puzynina, Svetlana.
In: Electronic Journal of Combinatorics, Vol. 26, No. 4, P4.15, 11.10.2019.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Aperiodic two-dimensional words of small abelian complexity
AU - Puzynina, Svetlana
PY - 2019/10/11
Y1 - 2019/10/11
N2 - In this paper we prove an abelian analog of the famous Nivat's conjecture linking complexity and periodicity for two-dimensional words: We show that if a two-dimensional recurrent word contains at most two abelian factors for each pair (n;m) of integers, then it has a periodicity vector. Moreover, we show that a two-dimensional aperiodic recurrent word must have more than two abelian factors infinitely often. On the other hand, there exist aperiodic recurrent words with abelian complexity bounded by 3, as well as aperiodic words having abelian complexity 1 for some pairs (m;n).
AB - In this paper we prove an abelian analog of the famous Nivat's conjecture linking complexity and periodicity for two-dimensional words: We show that if a two-dimensional recurrent word contains at most two abelian factors for each pair (n;m) of integers, then it has a periodicity vector. Moreover, we show that a two-dimensional aperiodic recurrent word must have more than two abelian factors infinitely often. On the other hand, there exist aperiodic recurrent words with abelian complexity bounded by 3, as well as aperiodic words having abelian complexity 1 for some pairs (m;n).
UR - http://www.scopus.com/inward/record.url?scp=85074024712&partnerID=8YFLogxK
UR - https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i4p15/7940
M3 - Article
AN - SCOPUS:85074024712
VL - 26
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
SN - 1077-8926
IS - 4
M1 - P4.15
ER -
ID: 48985690