A new characteristic property of rich words

Bucci, M., De Luca, A., Glen, A. and Zamboni, L.Q. (2009) A new characteristic property of rich words. Theoretical Computer Science, 410 (30-32). pp. 2860-2863.

PDF - Authors' Version Download (94kB)

Abstract

Originally introduced and studied by the third and fourth authors together with J. Justin and S. Widmer (2008), rich words constitute a new class of finite and infinite words characterized by containing the maximal number of distinct palindromes. Several characterizations of rich words have already been established. A particularly nice characteristic property is that all 'complete returns' to palindromes are palindromes. In this note, we prove that rich words are also characterized by the property that each factor is uniquely determined by its longest palindromic prefix and its longest palindromic suffix.