论文标题
平面色带图的局部对偶
Partial-duals for planar ribbon graphs
论文作者
论文摘要
2009年，Chmutov引入了功能区图$ G $的部分二元性。最近，Gross，Mansour和Tucker列举了属的所有可能的部分二对$ g $，并引入了色带图$ G的部分二偶属多项式。首先，我们为任何平面色带图获得了最大部分二偶属的公式，并对毛，曼苏尔和塔克的插值猜想给出了负面答案。然后，我们表明，平面色带图$ g-e $和$ g $的部分双偶属多项式之间存在复发关系。此外，还给出了两个相关的结果。这些复发关系提供了一些新的方法来计算某些平面色带图的部分双二二元多项式。此外，我们证明了某些部分双偶属分布的渐近正态性。
In 2009, Chmutov introduced the partial-duality for a ribbon graph $G$. Recently, Gross, Mansour and Tucker enumerated all possible partial-duals of $G$ by genus and introduced the partial-dual genus polynomial of a ribbon graph $G.$ This paper mainly enumerates partial-duals for planar ribbon graphs. First, we obtain a formula for the maximum partial-dual genus for any planar ribbon graph and give a negative answer to the interpolating conjecture of Gross, Mansour and Tucker. Then we show that there is a recurrence relation between the partial-dual genus polynomials of planar ribbon graphs $G-e$ and $G$. Furthermore, two related results are also given. These recurrence relations give new approaches to calculate the partial-genus dual polynomials for some planar ribbon graphs. In addition, we prove the asymptotic normality for some partial-dual genus distributions.
