Perfectly clustering words are one of many possible generalizations of Christoffel words. In this article, we propose a factorization of a perfectly clustering word on a n letters alphabet into a product of n-1 palindromes with a letter between each of them. This factorization allows us to generalize two combinatorial characterization of Christoffel words due to Pirillo (1999) and de Luca and Mignosi (1994).
@article{10_37236_12851,
author = {M\'elodie Lapointe and Christophe Reutenauer},
title = {Characterizations of perfectly clustering words},
journal = {The electronic journal of combinatorics},
year = {2025},
volume = {32},
number = {3},
doi = {10.37236/12851},
zbl = {8097636},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12851/}
}
TY - JOUR
AU - Mélodie Lapointe
AU - Christophe Reutenauer
TI - Characterizations of perfectly clustering words
JO - The electronic journal of combinatorics
PY - 2025
VL - 32
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12851/
DO - 10.37236/12851
ID - 10_37236_12851
ER -
%0 Journal Article
%A Mélodie Lapointe
%A Christophe Reutenauer
%T Characterizations of perfectly clustering words
%J The electronic journal of combinatorics
%D 2025
%V 32
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12851/
%R 10.37236/12851
%F 10_37236_12851
Mélodie Lapointe; Christophe Reutenauer. Characterizations of perfectly clustering words. The electronic journal of combinatorics, Tome 32 (2025) no. 3. doi: 10.37236/12851
