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{\bf Antonio Bernini, Luca Ferrari and Einar Steingr\'imsson}
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{\bf The M\"{o}bius Function of the Consecutive Pattern Poset}
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 An occurrence of a consecutive permutation pattern $p$ in a
  permutation $\pi$ is a segment of consecutive letters of $\pi$ whose
  values appear in the same order of size as the letters in $p$.  The
  set of all permutations forms a poset with respect to such pattern
  containment.  We compute the M\"obius function of intervals in this
  poset.  For most intervals our results give an immediate answer to
  the question.  In the remaining cases, we give a polynomial time
  algorithm to compute the M\"obius function.  In particular, we show
  that the M\"obius function only takes the values $-1$, $0$ and ~$1$.

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