The number of trees with a 1-factor
Discrete Mathematics
On an asymptotic method in enumeration
Journal of Combinatorial Theory Series A
Trees with 1-factors and oriented trees
Discrete Mathematics
Systems of functional equations
Random Structures & Algorithms - Special issue: average-case analysis of algorithms
Twelve countings with rooted plane trees
European Journal of Combinatorics
Coloring rules for finite trees, and probabilities of monadic second order sentences
Random Structures & Algorithms
Addendum to “Twelve countings with rooted plane trees”
European Journal of Combinatorics
Combinatorial Enumeration
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In a paper by Klazar, several counting examples for rooted plane trees were given, including matchings and maximal matchings. Apart from asymptotical analysis, it was shown how to obtain exact formulas for some of the countings by means of the Lagrange inversion formula. In this note, the results of Klazar are extended to formulas for matchings, maximal matchings and maximum matchings for three types of simply generated trees. Finally, edge coverings are considered and the results are compared.