Geodesic
On the Sperner property for the absolute order on complex reflection groups
Gaetz, Christian1 ; Gao, Yibo1
1 Department of Mathematics Massachusetts Institute of Technology Cambridge, MA USA
Algebraic Combinatorics, Tome 3 (2020) no. 3, pp. 791-800.

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Two partial orders on a reflection group W, the codimension order and the prefix order, are together called the absolute order Abs(W) when they agree. We show that in this case the absolute order on a complex reflection group has the strong Sperner property, except possibly for the Coxeter group of type Dn, for which this property is conjectural. The Sperner property had previously been established for the noncrossing partition lattice NCW [, ], a certain maximal interval in Abs(W), but not for the entire poset, except in the case of the symmetric group []. We also show that neither the codimension order nor the prefix order has the Sperner property for general complex reflection groups.

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DOI : 10.5802/alco.114
Classification : 20F55, 06A11, 06A07
Mots-clés : Absolute order, Sperner property, antichain, normalized flow, reflection group.

Gaetz, Christian 1 ; Gao, Yibo 1

1 Department of Mathematics Massachusetts Institute of Technology Cambridge, MA USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Gaetz, Christian; Gao, Yibo. On the Sperner property for the absolute order on complex reflection groups. Algebraic Combinatorics, Tome 3 (2020) no. 3, pp. 791-800. doi : 10.5802/alco.114. https://geodesic-test.mathdoc.fr/articles/10.5802/alco.114/

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