Article history: Received 12 September 2015 Accepted 21 December 2015 Available online xxxx Submitted by R. Brualdi MSC: primary 05E15 secondary 15A21

In this paper, for an arbitrary multiplicative functional f from the set of all upper triangular fuzzy matrices to the fuzzy algebra, we prove that there exist a multiplicative functional F and a functional G from the fuzzy algebra to the fuzzy algebra such that the image of an upper triangular fuzzy matrix under f can be represented as the product of all the images of its main diagonal element...

In this paper we reduce the problem concerning the number of connected components in the intersection of two real opposite open Schubert cells in SLn(R)/B to a purely combinatorial question in the space of upper triangular matrices with F2-valued entries. The crucial step of the reduction uses the parametrization of the space of real unipotent totally positive upper triangular matrices introduc...

We study two random walks on a group of upper triangular matrices. In each case, we give upper bound on the mixing time by using a stopping time technique.