Motivated by a conjecture of Frid, Puzynina, and Zamboni, we investigate infinite words with the property that for infinitely many $n$, every length-$n$ factor is a product of two palindromes. We show that every Sturmian word has this property, but this does not characterize the class of Sturmian words. We also show that the Thue—Morse word does not have this property. We investigate finite words with the maximal number of distinct palindrome pair factors and characterize the binary words that are not palindrome pairs but have the property that every proper factor is a palindrome pair.
@article{10_37236_5583,
author = {Adam Borchert and Narad Rampersad},
title = {Words with many palindrome pair factors},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5583},
zbl = {1327.68181},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5583/}
}
TY - JOUR
AU - Adam Borchert
AU - Narad Rampersad
TI - Words with many palindrome pair factors
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5583/
DO - 10.37236/5583
ID - 10_37236_5583
ER -
%0 Journal Article
%A Adam Borchert
%A Narad Rampersad
%T Words with many palindrome pair factors
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5583/
%R 10.37236/5583
%F 10_37236_5583
Adam Borchert; Narad Rampersad. Words with many palindrome pair factors. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5583
