2025/12/10 by Anna E. Frid, Frid, Anna E.
Computer Science · Mathematics · #03D40 #08A50 #20F10 #20M05 #68R15 #Advanced Algebra and Logic #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2512.10024
openalex publication_date 2025/12/10 · openalex created_date 2025/12/13 · openalex updated_date 2026/07/28
The palindromic length of a finite word w is defined as the minimal number of palindromes such that their product is w. Clearly, this function may take different values depending on if we consider w as an element a free semigroup or of a free group: for example, in the free semigroup, the palindromic length of abca is 4 (here every letter is a palindrome), and in the free group, it is 3 since abca=(aba)(a-1a-1)(aca). 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.