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

See the original article notice from the Numdam source

MR

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 D n , for which this property is conjectural. The Sperner property had previously been established for the noncrossing partition lattice NC W  [, ], 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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.114
Classification: 20F55, 06A11, 06A07
Keywords: 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Gaetz, Christian; Gao, Yibo. On the Sperner property for the absolute order on complex reflection groups. Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 791-800. doi: 10.5802/alco.114
@article{ALCO_2020__3_3_791_0,
     author = {Gaetz, Christian and Gao, Yibo},
     title = {On the {Sperner} property for the absolute order on complex reflection groups},
     journal = {Algebraic Combinatorics},
     pages = {791--800},
     year = {2020},
     publisher = {MathOA foundation},
     volume = {3},
     number = {3},
     doi = {10.5802/alco.114},
     mrnumber = {4113607},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.114/}
}
TY  - JOUR
AU  - Gaetz, Christian
AU  - Gao, Yibo
TI  - On the Sperner property for the absolute order on complex reflection groups
JO  - Algebraic Combinatorics
PY  - 2020
SP  - 791
EP  - 800
VL  - 3
IS  - 3
PB  - MathOA foundation
UR  - http://geodesic.mathdoc.fr/articles/10.5802/alco.114/
DO  - 10.5802/alco.114
LA  - en
ID  - ALCO_2020__3_3_791_0
ER  - 
%0 Journal Article
%A Gaetz, Christian
%A Gao, Yibo
%T On the Sperner property for the absolute order on complex reflection groups
%J Algebraic Combinatorics
%D 2020
%P 791-800
%V 3
%N 3
%I MathOA foundation
%U http://geodesic.mathdoc.fr/articles/10.5802/alco.114/
%R 10.5802/alco.114
%G en
%F ALCO_2020__3_3_791_0

Cited by Sources: