Canadian Mathematical Monographs, 1970, -121 pp.
My object has been to gather together various combinatorial results on labelled trees. The basic definitions are given in the first chapter; enumerative results are presented in the next five chapters, classified according to the type of argument involved; some probabilistic problems on random trees are treated in the last chapter. Some familiarity with matrices and generating functions is presupposed, in places, but much of the exposition should be accessible to anyone who knows something about finite mathematics or probability theory.
This material was originally prepared for a series of lectures I gave at the Twelfth Biennial Seminar of the Canadian Mathematical Congress at the University of British Columbia in August, 1969. I am indebted to Professors Ronald Руке and John J. McNamee for their invitation and encouragement.
Introduction.
Associating Sequences with Trees.
Inductive Arguments.
Applications of Generating Functions.
The Matrix Tree Theorem.
The Method of Inclusion and Exclusion.
Problems on Random Trees.
My object has been to gather together various combinatorial results on labelled trees. The basic definitions are given in the first chapter; enumerative results are presented in the next five chapters, classified according to the type of argument involved; some probabilistic problems on random trees are treated in the last chapter. Some familiarity with matrices and generating functions is presupposed, in places, but much of the exposition should be accessible to anyone who knows something about finite mathematics or probability theory.
This material was originally prepared for a series of lectures I gave at the Twelfth Biennial Seminar of the Canadian Mathematical Congress at the University of British Columbia in August, 1969. I am indebted to Professors Ronald Руке and John J. McNamee for their invitation and encouragement.
Introduction.
Associating Sequences with Trees.
Inductive Arguments.
Applications of Generating Functions.
The Matrix Tree Theorem.
The Method of Inclusion and Exclusion.
Problems on Random Trees.