We consider several probabilistic processes defining a random graph. One of these processes appeared recently in connection with a factorization problem in the symmetric group. For each process, we prove that the probability for the random graph to be a tree has an unexpectedly simple expression, which is independent of most parameters of the problem. This raises many open questions.
@article{10_37236_4954,
author = {Olivier Bernardi and Alejandro H. Morales},
title = {Some probabilistic trees with algebraic roots},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {2},
doi = {10.37236/4954},
zbl = {1336.05112},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4954/}
}
TY - JOUR
AU - Olivier Bernardi
AU - Alejandro H. Morales
TI - Some probabilistic trees with algebraic roots
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4954/
DO - 10.37236/4954
ID - 10_37236_4954
ER -
%0 Journal Article
%A Olivier Bernardi
%A Alejandro H. Morales
%T Some probabilistic trees with algebraic roots
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4954/
%R 10.37236/4954
%F 10_37236_4954
Olivier Bernardi; Alejandro H. Morales. Some probabilistic trees with algebraic roots. The electronic journal of combinatorics, Tome 23 (2016) no. 2. doi: 10.37236/4954
