The Bruhat Order on Symmetric Groups via Intrinsic Coverings of Compositions

Published 2 Feb 2022 in math.CO | (2202.00835v2)

Abstract: Lehmer's code defines a bijection between the symmetric group and the set of staircase compositions. In this paper, we characterize a poset structure on these compositions that is equivalent to the strong Bruhat order on the symmetric group. This construction is intrinsic and does not require any reference to the associated permutations.

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