{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T15:28:55Z","timestamp":1758814135488,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A word is abelian square-free if it does not contain two adjacent subwords which are permutations of each other. Over an alphabet $\\Sigma_k$ on $k$ letters, an abelian square-free word is maximal if it cannot be extended to the left or right by letters from $\\Sigma_k$ and remain abelian square-free. Michael Korn proved that the length $\\ell (k)$ of a shortest maximal abelian square-free word satisfies $4k-7\\leq \\ell(k)\\leq 6k-10$ for $k\\geq 6$. In this paper, we refine Korn's methods to show that $6k-29\\leq \\ell(k)\\leq 6k-12$ for $k\\geq 8$.<\/jats:p>","DOI":"10.37236\/1770","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:23:15Z","timestamp":1578720195000},"source":"Crossref","is-referenced-by-count":2,"title":["Improved Bounds on the Length of Maximal Abelian Square-Free Words"],"prefix":"10.37236","volume":"11","author":[{"given":"Evan M.","family":"Bullock","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,2,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:04:35Z","timestamp":1579323875000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1770","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,2,20]]},"article-number":"R17"}}