CAJ | 학술논문

本文研究了球面和射影平面上对偶无环不可分近三角剖分带根地图的以根面次和内面数为参数的计数问题,得到了这类地图在球面和射影平面上的计数函数满足的方程.还得到了射影平面上2连通地图一个参数的显示表达式和渐近估计式.
본문연구료구면화사영평면상대우무배불가분근삼각부분대근지도적이근면차화내면수위삼수적계수문제,득도료저류지도재구면화사영평면상적계수함수만족적방정.환득도료사영평면상2련통지도일개삼수적현시표체식화점근고계식.
In this paper we enumerate the rooted dual loopless nonseparable near-triangular maps on the sphere and the projective plane with the valency of root-face and the number of inner faces as parameters. Explicit expressions of enumerating functions are derived for such maps on the sphere and the projective plane. A parametric expression of the generating function is obtained for the rooted 2-connected triangular maps on the projective plane, from which asymptotics evaluations are derived.