scholarly journals A Class of Labeled Posets and the Shi Arrangement of Hyperplanes

1997 ◽  
Vol 80 (1) ◽  
pp. 158-162 ◽  
Author(s):  
Christos A Athanasiadis
Keyword(s):  
Arrangement Of Hyperplanes ◽  
Shi Arrangement

scholarly journals A simple bijection for the regions of the Shi arrangement of hyperplanes

1999 ◽  
Vol 204 (1-3) ◽  
pp. 27-39 ◽  
Author(s):  
Christos A. Athanasiadis ◽  
Svante Linusson
Keyword(s):  
Arrangement Of Hyperplanes ◽  
Shi Arrangement

scholarly journals Depth in an Arrangement of Hyperplanes

1999 ◽  
Vol 22 (2) ◽  
pp. 167-176 ◽  
Author(s):  
P. J. Rousseeuw ◽  
M. Hubert
Keyword(s):  
Arrangement Of Hyperplanes

scholarly journals The deligne complex of a real arrangement of hyperplanes

1993 ◽  
Vol 131 ◽  
pp. 39-65 ◽  
Author(s):  
Luis Paris
Keyword(s):  
Vector Space ◽  
Finite Family ◽  
Real Vector Space ◽  
Real Vector ◽  
Arrangement Of Hyperplanes

Let V be a real vector space. An arrangement of hyperplanes in V is a finite family of hyperplanes of V through the origin. We say that is essential if ∩H ∊H = {0}

scholarly journals Rich cells in an arrangement of hyperplanes

1995 ◽  
Vol 226-228 ◽  
pp. 567-575 ◽  
Author(s):  
I. Bárány ◽  
H. Bunting ◽  
D.G. Larman ◽  
J. Pach
Keyword(s):  
Arrangement Of Hyperplanes

scholarly journals The freeness of Ish arrangements

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Takuro Abe ◽  
Daisuke Suyama ◽  
Shuhei Tsujie
Keyword(s):  
Catalan Numbers ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Free Arrangement ◽  
International Audience ◽  
New Interpretation ◽  
Necessary And Sufficient ◽  
Shi Arrangement

International audience The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free L’arrangement Ish a été introduit par Armstrong pour donner une nouvelle interprétation des nombres $q; t$-Catalan de Garsia et Haiman. Armstrong et Rhoades ont montré qu’il y avait des ressemblances frappantes entre l’arrangement Shi et l’arrangement Ish et ont posé des conjectures. L’une d’elles est de savoir si l’arrangement Ish est un arrangement libre ou pas. Dans cet article, nous vérifions que l’arrangement Ish est supersoluble et donc libre. De plus, on donne une condition nécessaire et suffisante pour que l’arrangement Ish réduit soit libre.

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