Séminaire Lotharingien de Combinatoire, 82B.7 (2019), 12 pp.
Henri Mühle
Ballot-noncrossing partitions
Abstract.
Noncrossing partitions, Dyck paths, and 231-avoiding permutations are classical examples of Catalan objects, and they may be defined in terms of the symmetric group. Moreover, when we consider noncrossing partitions ordered by refinement and 231-avoiding permutations ordered by inclusion of inversion sets, then there is a close structural relationship between the two resulting posets. In this abstract we show that this connection, together with some other properties of these two posets, still holds in the generalized setting of (certain special) parabolic quotients of the symmetric group.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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