Subspace Arrangement Codes and Cryptosystems

2011 ◽  
Author(s):  
James A. Berg
Keyword(s):  
Subspace Arrangement

scholarly journals Characteristic varieties of arrangements

1999 ◽  
Vol 127 (1) ◽  
pp. 33-53 ◽  
Author(s):  
DANIEL C. COHEN ◽  
ALEXANDER I. SUCIU
Keyword(s):  
Tangent Cone ◽  
Identity Element ◽  
Direct Sum ◽  
Algebraic Torus ◽  
Irreducible Components ◽  
Fitting Ideal ◽  
Characteristic Varieties ◽  
Alexander Invariants ◽  
Pass Through ◽  
Subspace Arrangement

The kth Fitting ideal of the Alexander invariant B of an arrangement [Ascr ] of n complex hyperplanes defines a characteristic subvariety, Vk([Ascr ]), of the algebraic torus ([Copf ]*)n. In the combinatorially determined case where B decomposes as a direct sum of local Alexander invariants, we obtain a complete description of Vk([Ascr ]). For any arrangement [Ascr ], we show that the tangent cone at the identity of this variety coincides with [Rscr ]1k(A), one of the cohomology support loci of the Orlik–Solomon algebra. Using work of Arapura [1], we conclude that all irreducible components of Vk([Ascr ]) which pass through the identity element of ([Copf ]*)n are combinatorially determined, and that [Rscr ]1k(A) is the union of a subspace arrangement in [Copf ]n, thereby resolving a conjecture of Falk [11]. We use these results to study the reflection arrangements associated to monomial groups.

scholarly journals Étale cohomology of the complement of a linear subspace arrangement

2011 ◽  
Vol 9 (1) ◽  
pp. 119-149
Author(s):  
Andre Chatzistamatiou
Keyword(s):  
Linear Subspace ◽  
Cup Product ◽  
Etale Cohomology ◽  
Étale Cohomology ◽  
Subspace Arrangement

AbstractWe prove a formula for the cup product on the ℓ-adic cohomology of the complement of a linear subspace arrangement.

scholarly journals The homotopy type of the complement of a coordinate subspace arrangement

Topology ◽  
2007 ◽  
Vol 46 (4) ◽  
pp. 357-396 ◽  
Author(s):  
Jelena Grbić ◽  
Stephen Theriault
Keyword(s):  
Homotopy Type ◽  
Subspace Arrangement

Dimension Reduction Parameters for Leukemia Diagnostic based in Subspace Arrangement Segmentation

2014 ◽  
Vol 8 (6) ◽  
pp. 2789-2794
Author(s):  
Leticia Flores-Pulido ◽  
Gustavo Rodr�guez-G�mez ◽  
Jes�s A. Gonz�lez
Keyword(s):  
Dimension Reduction ◽  
Subspace Arrangement

scholarly journals The Homology of the Real Complement of a $k$-parabolic Subspace Arrangement

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Christopher Severs ◽  
Jacob A. White
Keyword(s):  
Morse Theory ◽  
Betti Numbers ◽  
Type A ◽  
Discrete Morse Theory ◽  
Type B ◽  
Combinatorial Interpretation ◽  
Subspace Arrangements ◽  
International Audience ◽  
Nous Utilisons ◽  
Subspace Arrangement

International audience The $k$-parabolic subspace arrangement, introduced by Barcelo, Severs and White, is a generalization of the well known $k$-equal arrangements of type-$A$ and type-$B$. In this paper we use the discrete Morse theory of Forman to study the homology of the complements of $k$-parabolic subspace arrangements. In doing so, we recover some known results of Björner et al. and provide a combinatorial interpretation of the Betti numbers for any $k$-parabolic subspace arrangement. The paper provides results for any $k$-parabolic subspace arrangement, however we also include an extended example of our methods applied to the $k$-equal arrangements of type-$A$ and type-$B$. In these cases, we obtain new formulas for the Betti numbers. L'arrangement $k$-parabolique, introduit par Barcelo, Severs et White, est une généralisation des arrangements, $k$-éguax de type $A$ et de type $B$. Dans cet article, nous utilisons la théorie de Morse discrète proposée par Forman pour étudier l'homologie des compléments d'arrangements $k$-paraboliques. Ce faisant, nous retrouvons les résultats connus de Bjorner et al. mais aussi nous fournissons une interprétation combinatoire des nombres de Betti pour des arrangements $k$-paraboliques. Ce papier fournit alors des résultats pour n'importe quel arrangement $k$-parabolique, cependant nous y présentons un exemple étendu de nos méthodes appliquées aux arrangements $k$-éguax de type $A$ et de type $B$. Pour ce cas, on obtient de nouvelles formules pour les nombres de Betti.

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