关于曲面无环根地图的普查(英文)

General Investigation of Loopless Maps on Surface

对于给定带根地图的根点次和棱数,提供了可定向、不可定向以及全体曲面上无环根地图的计数方程,这些微分方程都是Riccati型的.采用了一种新异的做法来求解该方程,进而由简单递推公式导出了带有两参数的无环根地图数,并给出了递推结果.与已发表的相关文献结论相比,形式上更加简洁,且可推广并应用于其他图类在不考虑亏格情况下的曲面计数.

For the given number of root-vertex degree and edges,the enumerative equations of rooted loopless maps on the surfaces including the orientable,nonorientable without regard to genus were provided.These differential equations are of Riccati type.A distinguishing approach to solve these corresponding calculative functions was expounded,and then the number of rooted loopless maps with two parameters was derived by the brief recursive formulae.Meanwhile,some consequences were given.These conclusions have much simpler form comparing with published research results.In addition,this method can be successfully extended to the cases of counting other classes of maps on surface without consideration of genus.