On Matula numbers
There are many methods to get a one-to-one correspondence between the set of natural numbers and the set of rooted trees. One of the methods uses the Matula numbers. Let \(T\) be a rooted tree, and let \(v\) be the root of \(T\). Then the Matula number \(n(T, v)\) is determined in the following recursive manner: (1) \(n(T, v)= 1\) for the single-vertex tree. (2) Let the root \(v\) of \(T\) be of degree \(d\). Then \(T\) can be considered as being obtained by joining the roots \(v_1,\dots, v_d\) of some rooted trees \(T_1,\dots, T_d\) and \[ n(T, v)= \prod^d_{i= 1} p_{n(T_i, v_i)}, \text{ where \(p_m\) denotes the \(m\)th prime number}. \] The paper lists known characterizations of Matula numbers and corresponding rooted trees, and determines the rooted trees with maximal Matula numbers.
scientific article; zbMATH DE number 895994