Paper
Small palindromic lengths in free groups and word equations with antimorphisms
Authors
Anna E. Frid
Abstract
The palindromic length of a finite word is defined as the minimal number of palindromes such that their product is . Clearly, this function may take different values depending on if we consider as an element a free semigroup or of a free group: for example, in the free semigroup, the palindromic length of is 4 (here every letter is a palindrome), and in the free group, it is 3 since .
In free semigroups, the palindromic length can clearly be computed, and there are fast algorithms for that. In free groups, the question is trickier. In this paper, we characterize words in the free group whose palindromic length is 2 and 3.