The maximum number of atoms of Bruhat intervals in the symmetric groups

  • Authors:

  • Masato Kobayashi

  • Affiliations:

  • -

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2011

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Abstract

We prove that the maximum number of (co)atoms of Bruhat intervals of the length n-1 in the symmetric group S"n is @?n^2/4@?. We show how to construct such an interval, explicitly making use of the subexpression property among bigrassmannian permutations together with the result by Adin-Roichman that the maximum of the down degree (the number of elements covered by a given permutation) in S"n is @?n^2/4@?.