Product decompositions of the symmetric group induced by separable permutations

Fan Wei

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


In this paper we consider the rank generating function of a separable permutation π in the weak Bruhat order on the two intervals [id,π] and [π,w0], where w0=n,n-1,..., 1. We show a surprising result that the product of these two generating functions is the generating function for the symmetric group with the weak order. We then obtain explicit formulas for the rank generating functions on [id,π] and [π,w0], leading to the rank-symmetry and unimodality of the two graded posets.

Original languageEnglish (US)
Pages (from-to)572-582
Number of pages11
JournalEuropean Journal of Combinatorics
Issue number4
StatePublished - May 2012

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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