{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:29:13Z","timestamp":1759336153158,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A power is a concatenation of $k$ copies of a word $u$, for a positive integer $k$; the power is also called a $k$-power and $k$ is its exponent. We prove that for any $k \\ge 2$, the maximum number of different non-empty $k$-power factors in a word of length $n$ is between $\\frac{n}{k-1}-\\Theta(\\sqrt{n})$ and $\\frac{n-1}{k-1}$. We also show that the maximum number of different non-empty power factors of exponent at least 2 in a length-$n$ word is at most $n-1$. Both upper bounds generalize the recent upper bound of $n-1$ on the maximum number of different square factors in a length-$n$ word by Brlek and Li (2022).<\/jats:p>","DOI":"10.37236\/11270","type":"journal-article","created":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T16:42:48Z","timestamp":1723135368000},"source":"Crossref","is-referenced-by-count":1,"title":["A Note on the Maximum Number of k-Powers in a Finite Word"],"prefix":"10.37236","volume":"31","author":[{"given":"Shuo","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub","family":"Pachocki","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jakub","family":"Radoszewski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,8,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i3p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T16:42:49Z","timestamp":1723135369000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i3p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,9]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,12]]}},"URL":"https:\/\/doi.org\/10.37236\/11270","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,8,9]]},"article-number":"P3.14"}}