5 papers
A central limit theorem for connected components of random coverings of manifolds with nilpotent fundamental groups
Abdelmalek Abdesselam
There is a well understood way of generating random coverings of a fixed manifold by sampling homomorphisms from the fundamental group of this manifold into the symmetric group. We…
A central limit theorem for a generalization of the Ewens measure to random tuples of commuting permutations
Abdelmalek Abdesselam, Shannon Starr
We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of G…
A combinatorial formula for the coefficients of multidimensional resultants
Abdelmalek Abdesselam
The classical multidimensional resultant can be defined as the, suitably normalized, generator of a projective elimination ideal in the ring of universal coefficients. This is the…
Proof of a conjecture by Starr and log-concavity for random commuting permutations
Abdelmalek Abdesselam
We prove a conjecture by Shannon Starr regarding the asymptotics for the number of tuples of commuting permutations with given number of joint orbits. These numbers generalize unsi…
Structure constants for simple Lie algebras from principal -triple
Abdelmalek Abdesselam, Alexander Thomas
For a simple complex Lie algebra , fixing a principal -triple and highest weight vectors induces a basis of as vector space. For $\mat…