Prüfer $d$-groups

Prüfer codes for acyclic hypertrees

We describe a new Prüfer code based on star-reductions which works for infinite acyclic hypertrees.

Curves and coherent Prüfer rings

Usual definitions of Dedekind domain are not well suited for an algorithmic treatment. Indeed, the notion of Noetherian rings is subtle from a constructive point of view, and to be able to get prime ideals involve strong hypotheses. For instance, if k is a field, even given explicitely, there is in general no method to factorize polynomials in k[X]. The work [2] analyses the notion of Dedekind ...

On the Locality of the Prüfer Code

The Prüfer code is a bijection between trees on the vertex set [n] and strings on the set [n] of length n − 2 (Prüfer strings of order n). In this paper we examine the ‘locality’ properties of the Prüfer code, i.e. the effect of changing an element of the Prüfer string on the structure of the corresponding tree. Our measure for the distance between two trees T, T ∗ is ∆(T, T ∗) = n − 1 − |E(T )...

On the Debate Concerning Evolutionary Search Using Prüfer Numbers

A generalized enumeration of labeled trees and reverse Prüfer algorithm

A leader of a tree T on [n] is a vertex which has no smaller descendants in T . Gessel and Seo showed that ∑ T ∈Tn u(# of leaders in T )c(degree of 1 in T ) = uPn−1(1, u, cu), which is a generalization of Cayley’s formula, where Tn is the set of trees on [n] and Pn(a, b, c)= c n−1 ∏ i=1 ( ia + (n− i)b+ c. Using a variation of the Prüfer code which is called a RP-code, we give a simple bijective...