{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,30]],"date-time":"2025-08-30T16:55:12Z","timestamp":1756572912350,"version":"3.40.4"},"reference-count":7,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100010665","name":"H2020 Marie Sk\u0142odowska-Curie Actions","doi-asserted-by":"publisher","award":["754462"],"award-info":[{"award-number":["754462"]}],"id":[{"id":"10.13039\/100010665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Graphs and Combinatorics"],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>An animal is a planar shape formed by attaching congruent regular polygons along their edges. In 1976, Harary and Harborth gave closed isoperimetric formulas for Euclidean animals. Here, we provide analogous formulas for hyperbolic animals. We do this by proving a connection between Sturmian words and the parameters of a discrete analogue of balls in the graph determined by hyperbolic tessellations. This reveals a complexity in hyperbolic animals that is not present in Euclidean animals.<\/jats:p>","DOI":"10.1007\/s00373-025-02900-1","type":"journal-article","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T17:46:06Z","timestamp":1739987166000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Isoperimetric Formulas for Hyperbolic Animals"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4788-8225","authenticated-orcid":false,"given":"\u00c9rika","family":"Rold\u00e1n","sequence":"first","affiliation":[]},{"given":"Rosemberg","family":"Toal\u00e1-Enr\u00edquez","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,19]]},"reference":[{"issue":"1","key":"2900_CR1","first-page":"1","volume":"1","author":"F Harary","year":"1976","unstructured":"Harary, F., Harborth, H.: Extremal animals. J. Combin. Inf. Syst. Sci. 1(1), 1\u20138 (1976)","journal-title":"J. Combin. Inf. Syst. Sci."},{"issue":"1","key":"2900_CR2","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1007\/s00026-022-00631-1","volume":"27","author":"G Malen","year":"2023","unstructured":"Malen, G., Rold\u00e1n, \u00c9., Toal\u00e1-Enr\u00edquez, R.: Extremal $$\\{$$p, q$$\\}$$-animals. Ann. Combin. 27(1), 169\u2013209 (2023)","journal-title":"Ann. Combin."},{"key":"2900_CR3","unstructured":"Malen, G., Rold\u00e1n, E., Toal\u00e1-Enr\u00edquez, R.: Extremal hyperbolic animals (2021). https:\/\/www.erikaroldan.net\/extremal-p-q-animals"},{"key":"2900_CR4","unstructured":"OEIS foundation Inc. The on-line encyclopedia of integer sequences (2022). https:\/\/oeis.org\/"},{"key":"2900_CR5","unstructured":"Rold\u00e1n, E., Toal\u00e1-Enr\u00edquez, R.: Isoperimetric formulas for hyperbolic animals. https:\/\/www.erikaroldan.net\/isoperimetric-formulas-for-hyperbolic-animals"},{"key":"2900_CR6","unstructured":"Shallit, J.: Characteristic words as fixed points of homomorphisms. Research Report CS-91-72, Department of Computer Science, University of Waterloo (1991)"},{"issue":"1","key":"2900_CR7","first-page":"1","volume":"6","author":"HJS Smith","year":"1876","unstructured":"Smith, H.J.S.: Note on continued fractions. Messenger Math. 6(1), 1\u201314 (1876)","journal-title":"Messenger Math."}],"container-title":["Graphs and Combinatorics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02900-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00373-025-02900-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-025-02900-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,3]],"date-time":"2025-05-03T06:16:55Z","timestamp":1746253015000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00373-025-02900-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,19]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["2900"],"URL":"https:\/\/doi.org\/10.1007\/s00373-025-02900-1","relation":{},"ISSN":["0911-0119","1435-5914"],"issn-type":[{"type":"print","value":"0911-0119"},{"type":"electronic","value":"1435-5914"}],"subject":[],"published":{"date-parts":[[2025,2,19]]},"assertion":[{"value":"13 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to disclose. The authors have no conflict of interest to declare relevant to this article\u2019s content. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial or non-financial interest in the subject matter or materials discussed in this manuscript. The authors have no financial or proprietary interests in any material discussed in this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"38"}}