Abstract
Let D k ( w ) be the multiset containing all factors of w of length k including repetitions. One of the main results is that if D k ( w ) = D k ( v ) for all k ≤ ⌊ | w | 2 ⌋ + 1 , then w = v . The bound ⌊ | w | 2 ⌋ + 1 is optimal; however we will also show that if D k ( w ) = D k ( v ) for all k ≤ ⌊ | w | 2 ⌋ , then w and v are structurally similar.
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