A new characteristic property of rich words

Bucci, M., De Luca, A., Glen, A. and Zamboni, L. (2008) A new characteristic property of rich words. In: 12th Mons Theoretical Computer Science Days (Journées Montoises d'Informatique Théorique), 27 - 30 August, Mons, Belgium.

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Abstract

Originally introduced and studied by the third and fourth authors (A. Glen and L.Q. Zamboni) 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.