On minimal factorizations of words as products of palindromes

2012/10/23 by Anna E. Frid, Frid, Anna E., Svetlana Puzynina +3
Computer Science · #05D10 #68R15 #Advanced Algebra and Logic #Algorithms and Data Compression #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1210.6179

openalex publication_date 2012/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a finite word u, we define its palindromic length |u|_pal to be the least number n such that u=v₁v₂... v_n with each v_i a palindrome. We address the following open question: Does there exist an infinite non ultimately periodic word w and a positive integer P such that |u|_palP. In particular, the result holds for all the k-power-free words and for the Sierpinski word.

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