2015/01/29 by Émilie Charlier, Emilie Charlier, Tero Harju +7 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #68R15 #Algorithms and Data Compression #DNA and Biological Computing #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #cs.DM #cs.FL #msc:68R15 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1501.07464
14 pages
arxiv created 2015/01/29 · openalex publication_date 2015/01/29 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A finite word u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many unbordered factors. We are interested in abelian and weak abelian analogues of this result; namely, we investigate the following question(s): Let w be an infinite word such that all sufficiently long factors are (weakly) abelian bordered; is w (weakly) abelian periodic? In the process we answer a question of Avgustinovich et al. concerning the abelian critical factorization theorem.