{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:02Z","timestamp":1753893842474,"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>It is conjectured that given positive integers $l$, $m$, $n$ with $l^{-1}+m^{-1}+n^{-1} &lt; 1$ and an integer $g \\geq 0$, the triangle group $\\Delta=\\Delta (l,m,n)=\\langle X, Y, Z | X^l=Y^m=Z^n=XYZ=1 \\rangle $ contains infinitely many subgroups of finite index and of genus $g$. A slightly stronger version of this conjecture is as follows: given positive integers $l$, $m$, $n$ with $l^{-1}+m^{-1}+n^{-1} &lt; 1$ and an integer $g \\geq 0$, there are infinitely many nonisomorphic compact orientable hypermaps of type $(l,m,n)$ and genus $g$. We prove that these conjectures are true when two of the parameters $l$, $m$, $n$ are equal, by showing how to construct appropriate hypermaps.<\/jats:p>","DOI":"10.37236\/420","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:59:43Z","timestamp":1578715183000},"source":"Crossref","is-referenced-by-count":0,"title":["Infinitely many Hypermaps of a given Type and Genus"],"prefix":"10.37236","volume":"17","author":[{"given":"Gareth A.","family":"Jones","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Pinto","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2010,11,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r148\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v17i1r148\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:22:14Z","timestamp":1579303334000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v17i1r148"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,11,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2010,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/420","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2010,11,5]]},"article-number":"R148"}}