On the least number of palindromes contained in an infinite word
Gabriele Fici, Luca Q. Zamboni
TL;DR
This paper explores the minimal number of palindromic substrings within infinite words, analyzing various cases including alphabet size and word periodicity to understand the underlying combinatorial structure.
Contribution
It provides new bounds and characterizations for the least number of palindromes in infinite words across different alphabet sizes and structural constraints.
Findings
Periodic words can have fewer palindromic factors than non-periodic ones.
The minimal number of palindromes varies with alphabet size and word properties.
Specific bounds are established for binary alphabets.
Abstract
We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then investigate the same problem when the alphabet has size two.
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