Block numbers of permutations and Schur-positivity

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The block number of a permutation is the maximal number of components in its expression as a direct sum. We show that the distribution of the set of left-toright-maxima over 321-avoiding permutations with a given block number k is equal
to the distribution of this set over 321-avoiding permutations with the last descent of the inverse permutation at position n − k. This result is analogous to the FoataSchützenberger equi-distribution theorem, and implies Schur-positivity of the quasisymmetric generating function of descent set over 321-avoiding permutations with a prescribed block number
Original languageAmerican English
Article number64
Number of pages12
JournalSeminaire Lotharingien de Combinatoire
StatePublished - 2017


  • Schur positivity
  • permutation statistics
  • Pattern avoidance
  • quasi-symmetric function


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