Twelve countings with rooted plane trees (Q674629)

The author considers twelve parameters that can be defined on rooted plane trees: the number of (1) antichains, (2) maximal antichains, (3) chains, (4) infima closed sets, (5) connected sets, (6) independent sets, (7) maximal independent sets, (8) brooms, (9) matchings, (10) maximal matchings, (11) linear extensions, and (12) drawings in or of a rooted plane tree. He uses generating functions to determine the behaviour of the expected values of these parameters over the set of all rooted plane trees with \(n\) nodes. Reviewer's remark: The author has submitted an addendum to this paper that contains additional comments and references pertaining to earlier work done on some of the problems considered.