On Abelian Circular Squares in Binary Words1
نویسندگان
چکیده
To the memory of Paul Erdd os and to his living heritage Abstract. An abelian square in a binary word is a pair of adjacent non-empty blocks of the same length, having the same number of 1s. An abelian circular square is an abelian square which is possibly wrapped around the word: the tail protruding from the right end of the word reappears at the left end. Two abelian circular squares are equivalent if they have the same length and contain the same number of ones. We prove that the longest word with only k inequivalent abelian circular squares contains 4k+2 bits and has the form (01) 2k+1 or its complement. Possible connections to tandem repeats in the human genome are pointed out.
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