Littlewood Richardson coefficients are structure constants appearing in the representation theory of the general linear groups (GLn). The main results of this paper are: 1. A strongly polynomial randomized approximation scheme for Littlewood-Richardson coefficients corresponding to indices sufficiently far from the boundary of the Littlewood Richardson cone. 2. A proof of approximate log-concav...

For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g∗. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sln orbital varieties are described by Young tableaux. In this paper we consider so called Richardson orbital varieties in sln. A Richardson orbital variety ...

— In this article, we propose a new method well suited for the calculation of unstable solutions of nonlinear eigenvalues problem. This method is derived from the classical Marder-Weitzner scheme (MW) which can be seen as a nonlinear Richardson method. First we adapt to (MW) the usual extension of the classical Linear Richardson scheme (LR) which consists in computing the relaxation parameter i...

High order fast sweeping methods have been developed recently in the literature to solve static Hamilton-Jacobi equations efficiently. Comparing with the first order fast sweeping methods, the high order fast sweeping methods are more accurate, but they often require additional numerical boundary treatment for several grid points near the boundary because of the wider numerical stencil. It is p...