An Inequality for the Number of Periods in a Word

We prove an inequality for the number of periods in a word [Formula: see text] terms length and its initial critical exponent. Next, we characterize all length-[Formula: prefix characteristic Sturmian lazy Ostrowski representation text], use this result to show that our is tight infinitely many words text]. propose two related measures periodicity infinite words. Finally, also consider special cases where overlap-free or squarefree.