an:06260086
Zbl 1289.05258
Long, Shude; Cai, Junliang
Enumeration of boundary cubic inner-forest maps
EN
Ars Comb. 108, 341-354 (2013).
00329535
2013
j
05C45 05C30
boundary cubic; enumerating function; functional equation; Lagrangian inversion
Summary: This paper investigates the number of boundary cubic inner-forest maps and presents some formulae for such maps with the size (number of edges) and the valency of the root-face as two parameters. Further, by duality, some corresponding results for rooted outer-planar maps are obtained. It is also an answer to the open problem in [\textit{W. Liu} et al., Discrete Appl. Math. 155, No. 13, 1678--1688 (2007; Zbl 1122.05029)] and corrects the result on boundary cubic inner-tree maps in that article.
Zbl 1122.05029