an:06401158
Zbl 1313.05177
Long, Shude; Cai, Junliang
Enumeration of rooted loopless Eulerian planar maps
EN
Adv. Math., Beijing 43, No. 3, 365-378 (2014).
00341172
2014
j
05C30 05C45
general Eulerian map; loopless Eulerian map; enumerating function; parametric expression; Lagrangian inversion
Summary: Although much work has been done on enumerating rooted planar maps since Tutte's pioneering works in early 1960s, many classes of maps with no loops are still untreated. In this paper, we enumerate rooted loopless Eulerian planar maps with three parameters: the valency of rooted vertex, the number of nonrooted vertices and the number of inner faces.