A new bijection on rooted forests

A new bijection on rooted forests

Erdos, P. L., A new bijection on rooted forests, Discrete Mathematics 111 (1993) 179-188. This paper extends the method due to Szekely and ErdBs (1989) on the enumeration of trees. A bijection is introduced on certain classes of rooted forests (more exactly, on the class of semilabelled forests). This method yields new easy proofs for some well-known theorems which use only elementary calculati...

A New Bijection between Natural Numbers and Rooted Trees∗

A bijection is defined recursively between the set of natural numbers and the set of finite rooted trees. It is based on the prime decomposition of a natural number and the rank of a prime. This bijection leads naturally to a canonical presentation of rooted trees. For trees in each of two classes, bounds are given for the number of nodes in terms of the number assigned to the tree.

A Bijection for Rooted Maps on Orientable Surfaces

The enumeration of maps and the study of uniform random maps have been classical topics of combinatorics and statistical physics ever since the seminal work of Tutte in the sixties. Following the bijective approach initiated by Cori and Vauquelin in the eighties, we describe a bijection between rooted maps, or rooted bipartite quadrangulations, on a surface of genus g and some simpler objects t...

A bijection for rooted maps on general surfaces

The multinomial distribution on rooted labeled forests

For a probability distribution (ps; s 2 S) on a nite set S, call a random forest F of rooted trees labeled by S (with edges directed away from the roots) a p-forest if given F has m edges the vector of out-degrees of vertices of F has a multinomial distribution with parameters m and (ps; s 2 S), and given also these out-degrees the distribution of F is uniform on all forests with the given out-...