{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:18Z","timestamp":1753893858855,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We show that, for any fixed genus $g$, the ordinary generating function for the genus $g$ partitions of an $n$-element set into $k$ blocks is algebraic. The proof involves showing that each such partition may be reduced in a unique way to a primitive partition and that the number of primitive partitions of a given genus is finite. We illustrate our method by finding the generating function for genus $2$ partitions, after identifying all genus $2$ primitive partitions, using a computer-assisted search.<\/jats:p>","DOI":"10.37236\/7632","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:04:23Z","timestamp":1578668663000},"source":"Crossref","is-referenced-by-count":1,"title":["Counting Partitions of a Fixed Genus"],"prefix":"10.37236","volume":"25","author":[{"given":"Robert","family":"Cori","sequence":"first","affiliation":[]},{"given":"G\u00e1bor","family":"Hetyei","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,11,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p26\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i4p26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:21:46Z","timestamp":1579234906000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i4p26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,2]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,10,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7632","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2018,11,2]]},"article-number":"P4.26"}}