{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:55Z","timestamp":1753889875033,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","issue":"Automata, Logic and Semantics","license":[{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"},{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>A morphic word is obtained by iterating a morphism to generate an infinite word, and then applying a coding. We characterize morphic words with polynomial growth in terms of a new type of infinite word called a $\\textit{zigzag word}$. A zigzag word is represented by an initial string, followed by a finite list of terms, each of which repeats for each $n \\geq 1$ in one of three ways: it grows forward [$t(1)\\ t(2)\\ \\dotsm\\ t(n)]$, backward [$t(n)\\ \\dotsm\\ t(2)\\ t(1)$], or just occurs once [$t$]. Each term can recursively contain subterms with their own forward and backward repetitions. We show that an infinite word is morphic with growth $\\Theta(n^k)$ iff it is a zigzag word of depth $k$. As corollaries, we obtain that the morphic words with growth $O(n)$ are exactly the ultimately periodic words, and the morphic words with growth $O(n^2)$ are exactly the multilinear words.<\/jats:p>","DOI":"10.23638\/dmtcs-22-1-3","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:56:17Z","timestamp":1743699377000},"source":"Crossref","is-referenced-by-count":0,"title":["A Characterization of Morphic Words with Polynomial Growth"],"prefix":"10.23638","volume":"vol. 22 no. 1","author":[{"given":"Tim","family":"Smith","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,2,6]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1903.09905v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1903.09905v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T16:56:17Z","timestamp":1743699377000},"score":1,"resource":{"primary":{"URL":"http:\/\/dmtcs.episciences.org\/5324"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,6]]},"references-count":0,"journal-issue":{"issue":"Automata, Logic and Semantics","published-online":{"date-parts":[[2020,2,6]]}},"URL":"https:\/\/doi.org\/10.23638\/dmtcs-22-1-3","relation":{"has-preprint":[{"id-type":"arxiv","id":"1903.09905v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1903.09905v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1903.09905","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1903.09905","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2020,2,6]]},"article-number":"5324"}}