Counting Outerplanar Maps

Ivan Geffner, Marc Noy

Abstract


A map is outerplanar if all its vertices lie in the outer face. We enumerate various classes of rooted outerplanar maps with respect to the number of edges and vertices. The proofs involve several bijections with lattice paths. As a consequence of our results, we obtain an efficient scheme for encoding simple outerplanar maps.


Keywords


Map enumeration; Outerplanar map; Dyck path

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