Some combinatorial results on smooth permutations

Shoni Gilboa, Erez Lapid

Research output: Contribution to journalArticlepeer-review


We show that any smooth permutation σ∈Sn is characterized by the set C(σ) of transpositions and 3-cycles in the Bruhat interval (Sn)≤σ, and that σ is the product (in a certain order) of the transpositions in C(σ). We also characterize the image of the map σ↦C(σ). As an application, we show that σ is smooth if and only if the intersection of (Sn)≤σ with every conjugate of a parabolic subgroup of Sn admits a maximum. This also gives another approach for enumerating smooth permutations and subclasses thereof. Finally, we relate covexillary permutations to smooth ones and rephrase the results in terms of the (co)essential set in the sense of Fulton.
Original languageAmerican English
Pages (from-to)303–354
JournalJournal of Combinatorics
Issue number2
StatePublished - 2021


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