Jacobi matrices with prescribed eigenvalues and diagonal elements
Jacobians of certain transformations of singular matrices
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.
Jacobsthal numbers and alternating sign matrices.
Jucys-Murphy elements and the unitary Weingarten function
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.