The genus distribution of cubic graphs and asymptotic number of rooted cubic maps with high genus
演講時段：週二上午10:30~12:00；演講地點：統計所308會議室
- 2022-12-06 (Tue.), 10:30 AM
- 統計所308會議室；茶 會：上午10：10。
- 實體與線上視訊同步進行。
- Prof. Jason (Zhicheng) Gao ( 高志成 教授 )
- School of Mathematics and Statistics, Carleton University, Canada
Abstract
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 >= 0) is asymptotically normal with mean and variance asymptotic to (1/2)(n − ln n) and (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, we 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 (3/pi)n! 6^n.
線上視訊請點選連結
線上視訊請點選連結
附件下載
最後更新日期：2022-11-29 09:33
回列表頁
