Let G be the group of n×n upper-triangular matrices with elements in a finite field and ones on the diagonal. This paper applies the character theory of Andre, Carter and Yan to analyze a natural random walk based on adding or subtracting a random row from the row above.

Let T be an operator-weighted shift whose weights are 2-by-2 matrices. We say that, given > 0, T is in the -canonical form if each weight is an upper triangular matrix (aij), with 0 ≤ a11, a22 ≤ 1 and a12 6= 0 implies a11, a22 < . We generalize this concept to operator-weighted shifts whose weights are n-by-n matrices and we show that every polynomially bounded weighted shift, whose weights are...

Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices.

Generators are found for the field of invariants of coadjoint representations for the Lie algebras that are factors of a unitriangular Lie algebra by some regular ideal.

An m by n sign pattern A is an m by n matrix with entries in {+,−, 0}. The sign pattern A requires a positive (resp. nonnegative) left inverse provided each real matrix with sign pattern A has a left inverse with all entries positive (resp. nonnegative). In this paper, necessary and sufficient conditions are given for a sign pattern to require a positive or nonnegative left inverse. It is also ...

In this paper we obtain appropriate necessary and sufficient conditions for |N, pn|k summability to imply that of |N,qn|s for 1< k≤ s<∞. As in [6] we make use of a result of Bennett [1], who has obtained necessary and sufficient conditions for a factorable matrix to map lk → ls. A factorable matrix A is one in which each entry ank = bnck. Weighted mean matrices are factorable. It will not be po...

We give several new characterizations of Riordan Arrays, the most important of which is: if fd n;k g n;k2N is a lower triangular array whose generic element d n;k linearly depends on the elements in a well-deened though large area of the array, then fd n;k g n;k2N is Riordan. We also provide some applications of these characterizations to the lattice path theory.

In this paper a result concerning summability factors theorem for lower triangular matrices is presented. This result generalized and extend the result of Savas [1].