{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:18:14Z","timestamp":1761621494795,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $(m,n)$.<\/jats:p>","DOI":"10.37236\/8580","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T06:04:41Z","timestamp":1578636281000},"source":"Crossref","is-referenced-by-count":2,"title":["Aperiodic Two-Dimensional Words of Small Abelian Complexity"],"prefix":"10.37236","volume":"26","author":[{"given":"Svetlana","family":"Puzynina","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2019,10,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p15\/7940","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i4p15\/7940","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:02:30Z","timestamp":1579233750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i4p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2019,10,11]]}},"URL":"https:\/\/doi.org\/10.37236\/8580","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2019,10,11]]},"article-number":"P4.15"}}