两类花束图的部分对偶欧拉亏格多项式  

Partial-dual Euler-genus Polynomials for Two Classes of Bouquets

作　　者：朱可夫 颜棋 ZHU Kefu;YAN Qi(School of Mathematical Sciences,Xiamen University,Xiamen,Fujian,361005,P.R.China;School of Mathematics,China University of Mining and Technology,Xuzhou,Jiangsu,221116,P.R.China;School of Mathematics and Statistics,Lanzhou University,Lanzhou,Gansu,730000,P.R.China)

机构地区：[1]厦门大学数学科学学院,福建厦门361005 [2]中国矿业大学数学学院,江苏徐州221116 [3]兰州大学数学与统计学院,甘肃兰州730000

出　　处：《数学进展》2024年第2期267-280,共14页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.12101600);中央高校基本科研业务费专项资金(No.2021QN1037)。

摘　　要：[European J.Combin.,2020,86:Paper No.103084,20 pp.]在带子图中引入了部分对偶欧拉亏格多项式的概念,并给出插值猜想,即任意不可定向带子图的部分对偶欧拉亏格多项式是插值的.[European J.Combin.,2022,102:Paper No.103493,7 pp.]给出了两类反例否定了插值猜想,这两类花束图含有的侧面环只有一条或者两条不可定向环.本文是在[European J.Combin.,2022,102:Paper No.103493,7 pp.]的基础上,进一步计算其它两类花束图的部分对偶欧拉亏格多项式,其中一类是非插值的,它的侧面环有任意条不可定向环;而另一类是插值的,它的侧面环有任意条可定向环和不可定向环.[European J.Combin.,2020,86:Paper No.103084,20 pp.]introduced the partial-dual Euler-genus polynomial of the ribbon graphs and gave the interpolating conjecture.That is,the partial-dual Euler-genus polynomial for any non-orientable ribbon graph is interpolating.In fact,[European J.Combin.,2022,102:Paper No.103493,7 pp.]have given two classes of counterexamples to prove that the conjecture is wrong which contain only one or two non-orientable side loops.On the basis of[European J.Combin.,2022,102:Paper No.103493,7 pp.],we further calculate the partial-dual Euler-genus polynomials of two other classes of bouquets.One is non-interpolating whose all side loops are non-orientable loops and the number of them can be chosen arbitrarily.The other is interpolating whose side loops are a combination of non-orientable loops and orientable loops,and the number of both can be chosen arbitrarily.

关 键 词：带子图 部分对偶 亏格 多项式 插值性 

分 类 号：O157.5[理学—数学]