Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Counting the types of squares rather than their occurrences,  consider the problem of bounding the number of distinct squares in a string. Fraenkel and Simpson?shod in 1998 that a string of length n contains at most 2 n distinct squares. Ilie presented in 2007 an asymptotic upper bound of 2 n - ? ( log n ) .  show that a string of length n contains at most ? 11 n / 6 ? distinct squares. This new upper bound is obtained by investigating the combinatorial structure of double squares and showing that a string of length n contains at most ? 5 n / 6 ? particular double squares. In addition, the established structural properties provide a novel proof of Fraenkel and Simpson's result.
['Antoine Deza', 'Frantisek Franek', 'Adrien Thierry']
I am writing a research paper on a idea How many double squares can a string contain
[{"from": "human", "value": "I am writing a research paper on a idea How many double squares can a string contain"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Counting the types of squares rather than their occurrences,  consider the problem of bounding the number of distinct squares in a string. Fraenkel and Simpson?shod in 1998 that a string of length n contains at most 2 n distinct squares. Ilie presented in 2007 an asymptotic upper bound of 2 n - ? ( log n ) .  show that a string of length n contains at most ? 11 n / 6 ? distinct squares. This new upper bound is obtained by investigating the combinatorial structure of double squares and showing that a string of length n contains at most ? 5 n / 6 ? particular double squares. In addition, the established structural properties provide a novel proof of Fraenkel and Simpson's result."}]