Abstract
A Halin map is a kind of planar maps oriented by a tree. In this paper the rooted halin maps with the vertex, partitions as parameters are enumerated such that a famous results on rooted trees due to Harary, Prins, and Tutte is deduced as a special case. Further, by using Lagrangian inversion to obtain a number of summation free formulae directly, the various kinds of rooted Halin maps with up to three parameters have been counted.
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References
Harary, F., Prins, G. and Tutte, W. T., The number of plane trees, Indag. Math., 1964, 26: 319–329.
Liu Yanpei, Enumerative Theory of Maps, Kluwer, AP., Boston, 1998.
Liu Yanpei, Embeddibility in Graphs, Kluwer, AP., Boston, 1995.
Tutte, W. T., A census of planar maps, Canad. J. Math., 1963, 15: 249–271.
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The paper supported by the National Natural Science Foundation of China (19701002).
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Han, R., Yanpei, L. Enumeration of rooted planar halin maps. Appl. Math. Chin. Univ. 14, 117–121 (1999). https://doi.org/10.1007/s11766-999-0063-5
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DOI: https://doi.org/10.1007/s11766-999-0063-5