OFFSET
0,2
COMMENTS
Some boundary mutually non-adjacent nodes of valency 2 are marked as singular; (boundary) edges incident to them are also called singular. The maps are considered up to rotations and reflections. Rooting means distinguishing a non-singular edge, an end and an internal side of it. n is the number of internal edges plus half of the number of non-singular boundary edges.
No formula is known. For any generalized quadrangular dissection, s==n (mod 2), where s is the number of singular nodes.
LINKS
V. A. Liskovets, A reductive technique for enumerating nonisomorphic planar maps, Discr. Math., v.156 (1996), 197-217.
EXAMPLE
The four rooted generalized quadrangular dissections of weight 1 are
...................____......____..
.X<---X..X---<X.../....\..../....\.
.|....|..|....|..X<--X..O..X--<X..O
.|....|..|....|...\____/....\____/.
.X----O..X----O....................
where O is the singular node and -> is the rooted edge-end.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Valery A. Liskovets, Dec 03 2003
STATUS
approved