{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:09Z","timestamp":1753893789774,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $C_{n,g}$ be the number of rooted cubic maps with $2n$ vertices on the orientable surface of genus $g$. We show that the sequence $(C_{n,g}:g\\ge 0)$ is asymptotically normal with mean and variance asymptotic to $(1\/2)(n-\\ln n)$\u00a0and $(1\/4)\\ln n$, respectively. We derive an asymptotic expression for $C_{n,g}$ when $(n-2g)\/\\ln n$ lies in any closed subinterval of $(0,1)$.Using rotation systems and Bender's theorem about generating functions with fast-growing coefficients,\u00a0we derive simple asymptotic expressions for the numbers of rooted regular maps, disregarding the genus. In particular, we show that the number of rooted cubic maps with $2n$ vertices, disregarding the genus, is asymptotic to\u00a0$\\frac{3}{\\pi}\\,n!6^n$.<\/jats:p>","DOI":"10.37236\/11533","type":"journal-article","created":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T16:38:36Z","timestamp":1718296716000},"source":"Crossref","is-referenced-by-count":0,"title":["The Genus Distribution of Cubic Graphs and Asymptotic Number of Rooted Cubic Maps with High Genus"],"prefix":"10.37236","volume":"31","author":[{"given":"Zhicheng","family":"Gao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2024,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p49\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i2p49\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T16:38:37Z","timestamp":1718296717000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i2p49"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2024,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/11533","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,6,14]]},"article-number":"P2.49"}}