Results 41 to 50 of about 94 (68)

Electrical Networks, Hyperplane Arrangements and Matroids [PDF]

, 2019
This thesis introduces a class of hyperplane arrangements, called Dirichlet arrangements, arising from electrical networks with Dirichlet boundary conditions.
Lutz, Robert
core  

On The Class Of Factored Arrangements

, 2016
The first main objective of the work was to create a combinatorial answer to an essential question; "How Terao generalization of the class of supersolvable arrangements preserved the tensor factorization of the O-S algebra?", by finding a relation among ...
M. Ali, Hana', Abd-Kareem, Hawra'a H.
core   +1 more source

Koszulity, supersolvability, and Stirling representations

Supersolvable hyperplane arrangements and matroids are known to give rise to certain Koszul algebras, namely their Orlik-Solomon algebras and graded Varchenko-Gel'fand algebras. We explore how this interacts with group actions, particularly for the braid
Reiner, Victor, Sundaram, Sheila, Almousa, Ayah   +2 more
core   +1 more source

Lower central series and free resolutions of hyperplane arrangements

, 2008
. If M is the complement of a hyperplane arrangement, and A = H ∗ (M, k) is the cohomology ring of M over a field of characteristic 0, then the ranks, φk, of the lower central series quotients of π1(M) can be computed from the Betti numbers, bii = dim ...
Alexander, I. Suciu, Henry K. Schenck
core  

Convex Geometry of Building Sets

Building sets were introduced in the study of wonderful compactifications of hyperplane arrangement complements and were later generalized to finite meet-semilattices. Convex geometries, the duals of antimatroids, offer a robust combinatorial abstraction
Backman, Spencer, Danner, Rick
core   +1 more source

Lower central series and free resolutions of hyperplane arrangements

, 2002
If $M$ is the complement of a hyperplane arrangement, and $A=H^*(M,\k)$ is the cohomology ring of $M$ over a field of characteristic 0, then the ranks, $\phi_k$, of the lower central series quotients of $\pi_1(M)$ can be computed from the Betti numbers, $
Alexander I. Suciu, Henry K. Schenck
core  

Supersolvable posets and fiber-type arrangements

We develop a theory of modularity and supersolvability for chain-finite geometric posets, extending that of Stanley for finite lattices and building a new connection between combinatorics and topology.
Delucchi, Emanuele, Bibby, Christin
core  

Non-K(pi,1) arrangements

This thesis, supervised by Professor Filippo Gianluca Callegaro, addresses the problem of hyperplane arrangements that are not K(pi,1). I have analysed the following works: - The papers by Hattori (1976) and Salvetti (1987) on the non-asphericity of ...
TAVANO, MARCO
core  

On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangements

On an explicit correspondence between nbc-basis, chambers and minimal complex for real supersolvable arrangements
In this paper we give a very natural description of the bijections between the set of cells in the minimal CW-complex homotopy equivalent to the complement of a complexified real supersolvable arrangement A, the nbc-basis of the Orlik-Solomon algebra associated to A and the set of chambers of A.
openaire  

On supersolvable and nearly supersolvable line arrangements [PDF]

Journal of Algebraic Combinatorics, 2018
v.3, a version of the Slope Problem, valid over the real and the complex numbers as well, is obtained, see Thm. 1.1 and Thm.
Alexandru Dimca, Gabriel Sticlaru, Dimca Alexandru   +2 more
exaly   +4 more sources