Discrete Mathematics
On a reconstruction problem for sequences
Journal of Combinatorial Theory Series A
Theoretical Computer Science
Reconstruction from subsequences
Journal of Combinatorial Theory Series A
Connections between subwords and certain matrix mappings
Theoretical Computer Science - The art of theory
Subword conditions and subword histories
Information and Computation
Unavoidable regularities in long words with bounded number of symbol occurrences
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Discrete Applied Mathematics
Unavoidable regularities in long words with bounded number of symbol occurrences
Journal of Combinatorial Optimization
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We study some properties of palindromic (scattered) subwords of binary words. In view of the classical problem on subwords, we show that the set of palindromic subwords of a word characterizes the word up to reversal. Since each word trivially contains a palindromic subword of length at least half of its length-a power of the prevalent letter-we call a word that does not contain any palindromic subword longer than half of its length minimal palindromic. We show that every minimal palindromic word is abelian unbordered, that is, no proper suffix of the word can be obtained by permuting the letters of a proper prefix. We also propose to measure the degree of palindromicity of a word w by the ratio |rws|/|w|, where the word rws is minimal palindromic and rs is as short as possible. We prove that the ratio is always bounded by four, and construct a sequence of words that achieves this bound asymptotically.