  We are interested in the maximal number of distinct squares in a word. This
problem was introduced by Fraenkel and Simpson, who presented a bound of 2n for
a word of length n, and conjectured that the bound was less than n. Being that
the problem is on repetitions, their solution relies on Fine and Wilf's
Periodicity lemma. Ilie then refined their result and presented a bound of
2n-O(log n). Lam used an induction to get a bound of 95n/48. Deza, Franek and
Thierry achieved a bound of 11n/6 through a combinatorial approach. Using the
properties of the core of the interrupt, presented by Thierry, we refined here
the combinatorial structures exhibited by Deza, Franek and Thierry to offer a
bound of 3n/2.
