In this paper, we show how to compute, using Fitting ideals, the nonfree locus of the moduli
space of arrangements of a rank $3 $ simple matroid, ie, the subset of all points of the …

The Catalan numbers are one of the most ubiquitous and fascinating sequences of
enumerative combinatorics (Stanley), in particular they count the number of non-crossing …

Suppose that W is a finite, unitary reflection group acting on the complex vector space V. Let
𝒜= 𝒜 (W) be the associated hyperplane arrangement of W. Terao [J. Fac. Sci. Univ. Tokyo 27 …

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 …

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 …

Abstract In 2006 Sommers and Tymoczko defined so called arrangements of ideal type AI
stemming from ideals I in the set of positive roots of a reduced root system. They showed in a …

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 …

Extending earlier work by Sommers and Tymoczko, in 2016, Abe, Barakat, Cuntz, Hoge, and
Terao established that each arrangement of ideal type 𝒜 ℐ stemming from an ideal ℐ in the …

Suppose that W is a finite, unitary, reflection group acting on the complex vector space V. Let
A= A (W) be the associated hyperplane arrangement of W. Terao has shown that each such …

Abstract In 1962, Fadell and Neuwirth showed that the configuration space of the braid
arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn …