Séminaire Lotharingien de Combinatoire, 82B.35 (2019), 8 pp.

Christian Gaetz and Yibo Gao

The weak Bruhat order on the symmetric group is Sperner

Abstract. We construct a simple combinatorially-defined representation of sl2 which respects the order structure of the weak order on the symmetric group. This is used to resolve the longstanding open problem of showing that the weak order has the strong Sperner property, and is therefore a Peck poset.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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