Block decomposition of permutations and Schur-positivity

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Abstract

The block number of a permutation is the maximum number of components in its expression as a direct sum. We show that, for 321-avoiding permutations, the set of left-to-right maxima has the same distribution when the block number is assumed to be k, as when the last descent of the inverse is assumed to be at position n- k. This result is analogous to the Foata–Schützenberger equidistribution theorem, and implies that the quasi-symmetric generating function of the descent set over 321-avoiding permutations with a prescribed number of blocks is Schur-positive.

Original languageEnglish
Pages (from-to)603-622
Number of pages20
JournalJournal of Algebraic Combinatorics
Volume47
Issue number4
DOIs
StatePublished - 1 Jun 2018

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.

Keywords

  • Block number
  • Equidistribution
  • Schur-positivity

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