Partial-dual Euler-genus polynomials for two classes of bouquets  

作　　者：Kefu ZHU Qi YAN 

机构地区：[1]School of Mathematical Sciences,Xiamen University,Xiamen 361005,China [2]School of Mathematics,China University of Mining and Technology,Xuzhou 221116,China [3]School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,China

出　　处：《Frontiers of Mathematics in China》2024年第5期299-315,共17页中国高等学校学术文摘·数学（英文）

摘　　要：[European J.Combin.,2020,86:Paper No.103084,20 pp.]introduced the concept of partial-dual Euler-genus polynomial in the ribbon graphs and gave the interpolation 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.]gave two classes of counterexamples to deny the conjecture,and only one or two of the side loops contained in the two classes of bouquets were non-orientable.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 side loop has an arbitrary number of non-orientable loops.The other is interpolating,whose side loop has an arbitrary number of both non-orientable loops and orientable loops.

关 键 词：Ribbon graph partial-dual GENUS polynomial interpolating 

分 类 号：O17[理学—数学]