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Intervals and factors in the Bruhat order

Abstract : In this paper we study those generic intervals in the Bruhat order of the symmetric group that are isomorphic to the principal order ideal of a permutation w, and consider when the minimum and maximum elements of those intervals are related by a certain property of their reduced words. We show that the property does not hold when w is a decomposable permutation, and that the property always holds when w is the longest permutation.
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Bridget Eileen Tenner. Intervals and factors in the Bruhat order. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no. 1 (1), pp.383—-396. ⟨10.46298/dmtcs.2110⟩. ⟨hal-01196854⟩

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