Geodesic
Counting 2-connected 4-regular maps on the projective plane
The electronic journal of combinatorics, Tome 21 (2014) no. 2
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In this paper the number of rooted (near-) 4-regular maps on the projective plane are investigated with respect to the root-valency, the number of edges, the number of inner faces, the number of nonroot-vertex-loops, the number of nonroot-vertex-blocks. As special cases, formulae for several types of rooted 4-regular maps such as 2-connected 4-regular projective planar maps, rooted 2-connected (connected) 4-regular projective planar maps without loops are also presented. Several known results on the number of 4-regular maps on the projective plane are also concluded. Finally, by use of Darboux's method, very nice asymptotic formulae for the numbers of those types of maps are given.
DOI : 10.37236/4038
Classification : 05C30, 05C10, 05C45, 05C40
Mots-clés : rooted near-4-regular map, Lagrangian inversion, enumerating function, asymptotic 
@article{10_37236_4038,
     author = {Shude Long and Han Ren},
     title = {Counting 2-connected 4-regular maps on the projective plane},
     journal = {The electronic journal of combinatorics},
     year = {2014},
     volume = {21},
     number = {2},
     doi = {10.37236/4038},
     zbl = {1300.05131},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/4038/}
}
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Shude Long; Han Ren. Counting 2-connected 4-regular maps on the projective plane. The electronic journal of combinatorics, Tome 21 (2014) no. 2. doi: 10.37236/4038

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