scholarly journals Multiple addition, deletion and restriction theorems for hyperplane arrangements

2019 ◽  
Vol 147 (11) ◽  
pp. 4835-4845 ◽  
Author(s):  
Takuro Abe ◽  
Hiroaki Terao
Keyword(s):  
Hyperplane Arrangements ◽  
Restriction Theorems ◽  
Multiple Addition

scholarly journals MAT-free Reflection Arrangements

10.37236/8820 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Michael Cuntz ◽  
Paul Mücksch
Keyword(s):  
Addition Theorem ◽  
Hyperplane Arrangements ◽  
Complex Reflection ◽  
Multiple Addition

We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat,  Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent generalization of the Multiple Addition Theorem by Abe and Terao. We give classifications of the irreducible complex reflection arrangements which are MAT-free respectively MAT2-free. Furthermore, we ask some questions concerning relations to other classes of free arrangements. 

RESTRICTION THEOREMS IN REAL ANALYSIS

1994 ◽  
Vol 20 (2) ◽  
pp. 510 ◽  
Author(s):  
Brown
Keyword(s):  
Real Analysis ◽  
Restriction Theorems

RESTRICTION THEOREMS IN REAL ANALYSIS

1994 ◽  
Vol 20 (2) ◽  
pp. 411
Author(s):  
Brown
Keyword(s):  
Real Analysis ◽  
Restriction Theorems

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

scholarly journals The Tutte polynomial of symmetric hyperplane arrangements

2020 ◽  
Vol 29 (03) ◽  
pp. 2050004
Author(s):  
Hery Randriamaro
Keyword(s):  
Hyperplane Arrangement ◽  
Dual Graph ◽  
Tutte Polynomial ◽  
Hyperplane Arrangements ◽  
Weyl Groups ◽  
Reflection Groups ◽  
Tutte Polynomials ◽  
One Year ◽  
The One ◽  
Definition Of

The Tutte polynomial is originally a bivariate polynomial which enumerates the colorings of a graph and of its dual graph. Ardila extended in 2007 the definition of the Tutte polynomial on the real hyperplane arrangements. He particularly computed the Tutte polynomials of the hyperplane arrangements associated to the classical Weyl groups. Those associated to the exceptional Weyl groups were computed by De Concini and Procesi one year later. This paper has two objectives: On the one side, we extend the Tutte polynomial computing to the complex hyperplane arrangements. On the other side, we introduce a wider class of hyperplane arrangements which is that of the symmetric hyperplane arrangements. Computing the Tutte polynomial of a symmetric hyperplane arrangement permits us to deduce the Tutte polynomials of some hyperplane arrangements, particularly of those associated to the imprimitive reflection groups.

Multiple addition bioassay of Tjeukemeer water

Hydrobiologia ◽  
1982 ◽  
Vol 88 (3) ◽  
pp. 233-244 ◽  
Author(s):  
H. de Haan ◽  
J. B. W. Wanders ◽  
J. R. Moed
Keyword(s):  
Multiple Addition

scholarly journals Chitosan multiple addition enhances laccase production from Trametes versicolor

2015 ◽  
Vol 38 (10) ◽  
pp. 1973-1981 ◽  
Author(s):  
Abiodun Emmanuel Adekunle ◽  
Feng Wang ◽  
Jianhua Hu ◽  
Anzhou Ma ◽  
Chen Guo ◽  
...  
Keyword(s):  
Trametes Versicolor ◽  
Laccase Production ◽  
Multiple Addition
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