## 31 Citations

### Inductively Free Multiderivations of Braid Arrangements

- Mathematics
- 2015

The reflection arrangement of a Coxeter group is a well-known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such reflection…

### Inductively Free Multiderivations of Braid Arrangements

- MathematicsAnnals of Combinatorics
- 2016

The reflection arrangement of a Coxeter group is a well-known instance of a free hyperplane arrangement. In 2002, Terao showed that equipped with a constant multiplicity each such reflection…

### Combinatorics of free and simplicial line arrangements

- Mathematics
- 2018

We study the combinatorics of free and simplicial line arrangements. After some preparation, we start by proving the Dirac Motzkin Conjecture for line arrangements whose characteristic polynomials…

### Combinatorial simpliciality of arrangements of hyperplanes

- Mathematics
- 2013

We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangement in the projective…

### A simplicial complex of Nichols algebras

- Mathematics
- 2015

We translate the concept of restriction of an arrangement in terms of Hopf algebras. In consequence, every Nichols algebra gives rise to a simplicial complex decorated by Nichols algebras with…

### A simplicial complex of Nichols algebras

- MathematicsMathematische Zeitschrift
- 2016

We translate the concept of restriction of an arrangement in terms of Hopf algebras. In consequence, every Nichols algebra gives rise to a simplicial complex decorated by Nichols algebras with…

### Supersolvable orders and inductively free arrangements

- Mathematics
- 2017

Abstract In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results…

### Nice Reflection Arrangements

- MathematicsElectron. J. Comb.
- 2016

It is deduced that the class of all inductively factored reflection arrangements coincides with the supersolvable reflection arrangements.

## References

SHOWING 1-10 OF 15 REFERENCES

### Crystallographic arrangements: Weyl groupoids and simplicial arrangements

- Mathematics
- 2011

We introduce the simple notion of a ‘crystallographic arrangement’ and prove a one‐to‐one correspondence between these arrangements and the connected simply connected Cartan schemes for which the…

### Coxeter arrangements are hereditarily free

- Mathematics
- 1993

. A Coxeter arrangement is the set of reflecting hyperplanes in the reflection representation of a finite Coxeter group. Arnold and Saito showed that every Coxeter arrangement is free. We prove that…

### Finite Weyl groupoids

- Mathematics
- 2010

Using previous results concerning the rank two and rank three cases, all connected simply connected Cartan schemes for which the real roots form a finite irreducible root system of arbitrary rank are…

### AN AXIOMATIC SETUP FOR ALGORITHMIC HOMOLOGICAL ALGEBRA AND AN ALTERNATIVE APPROACH TO LOCALIZATION

- Mathematics
- 2011

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian…

### Commutative Algebra I

- Mathematics
- 2012

1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed

### SINGULAR: a computer algebra system for polynomial computations

- Mathematics, Computer ScienceACCA
- 2009

SINGULAR is a specialized computer algebra system for polynomial computations with emphasize on the needs of commutative algebra, algebraic geometry, and singularity theory, which features one of the fastest and most general implementations of various algorithms for computing standard resp.

### D-67653 Kaiserslautern, Germany E-mail address: cuntz@mathematik.uni-kl

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