The Shift-Match Number and String Matching Probabilities for Binary   Sequences
  We define the ``shift-match number'' for a binary string and we compute the probability of occurrence of a given string as a subsequence in longer strings in terms of its shift-match number. We thus prove that the string matching probabilities depend not only on the length of shorter strings, but also on the equivalence class of the shorter string determined by its shift-match number. 
A.H. Bilge, A. Erzan and D. Balcan