Palindromic rich words and run-length encodings
Chuan Jun Guo, Jeffrey O. Shallit, Arseny M. Shur · Information Processing Letters · 2016
A length n word is (palindromic) rich if it contains the maximum possible number, which is n , of distinct non-empty palindromic factors. We prove both necessary and sufficient conditions for richness in terms of run-length encodings of words. Relating sufficient conditions to integer partitions, we prove a lower bound of order C n , where C ≈ 37.6 , on the growth function of the language of binary rich words. From experimental study we suggest that this growth function actually grows more slowly than n n , which makes our lower bound quite reasonable.