Geodesic
On noncrossing and nonnesting partitions for classical reflection groups
The electronic journal of combinatorics, Tome 5 (1998)
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The number of noncrossing partitions of $\{1,2,\ldots,n\}$ with fixed block sizes has a simple closed form, given by Kreweras, and coincides with the corresponding number for nonnesting partitions. We show that a similar statement is true for the analogues of such partitions for root systems $B$ and $C$, defined recently by Reiner in the noncrossing case and Postnikov in the nonnesting case. Some of our tools come from the theory of hyperplane arrangements.
DOI : 10.37236/1380
Classification : 05A18, 05A15
Mots-clés : noncrossing partitions, nonnesting partitions, root systems, hyperplane arrangements 
@article{10_37236_1380,
     author = {Christos A. Athanasiadis},
     title = {On noncrossing and nonnesting partitions for classical reflection groups},
     journal = {The electronic journal of combinatorics},
     year = {1998},
     volume = {5},
     doi = {10.37236/1380},
     zbl = {0898.05004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1380/}
}
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%A Christos A. Athanasiadis
%T On noncrossing and nonnesting partitions for classical reflection groups
%J The electronic journal of combinatorics
%D 1998
%V 5
%U http://geodesic.mathdoc.fr/articles/10.37236/1380/
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Christos A. Athanasiadis. On noncrossing and nonnesting partitions for classical reflection groups. The electronic journal of combinatorics, Tome 5 (1998). doi: 10.37236/1380

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