Irreducible Toeplitz and Hankel matrices.
Through tropical normal idempotent matrices, we introduce isocanted alcoved polytopes, computing their -vectors and checking the validity of the following five conjectures: Bárány, unimodality, , flag and cubical lower bound (CLBC). Isocanted alcoved polytopes are centrally symmetric, almost simple cubical polytopes. They are zonotopes. We show that, for each dimension, there is a unique combinatorial type. In dimension , an isocanted alcoved polytope has vertices, its face lattice is the lattice...
In this study various Jacobians of transformations of singular random matrices are found. An alternative proof of Uhlig's first conjecture (Uhlig (1994)) is proposed. Furthermore, we propose various extensions of this conjecture under different singularities. Finally, an application of the theory of singular distributions is discussed.
We give a sufficient condition under which any Jordan automorphism of a triangular algebra is either an automorphism or an anti-automorphism.
We describe an approach to the unitary Weingarten function based on the JM elements of symmetric group algebras. When combined with previously known properties of the Weingarten function, this gives a surprising connection with the Moebius function of the lattice of noncrossing partitions.