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...

Let A denote the alternation limit algebra, studied by Hopenwasser and Power, and by Poon, which is the closed direct limit of upper triangular matrix algebras determined by refinement embeddings of multiplicity rk and standard embeddings of multiplicity sk. It is shown that the quotient of the isometric automorphism group by the approximately inner automorphisms is the abelian group ZZ where d...

We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an efficient scheme for rendering triangulated manifolds by graphics hardware. We also show that the Hamiltonian Cycle problem is NP-Complete for planar subcubic graphs of arbitrarily high girth. As a by-product we prove that there exist tri-Hamiltonian planar subcubic graphs of arbitrarily high gir...

Given a matrix M over a ring K, a target rank r and a bound k, we want to decide whether the rank of M can be brought down to below r by changing at most k entries of M . This is a decision version of the well-studied notion of matrix rigidity. We examine the complexity of the following related problems and obtain completeness results for small (counting logspace or smaller) classes: (a) comput...

The degree diameter problem involves finding the largest graph (in terms of number of vertices) subject to constraints on the degree and the diameter of the graph. Beyond the degree constraint there is no restriction on the number of edges (apart from keeping the graph simple) so the resulting graph may be thought of as being embedded in the complete graph. In a generalisation of this problem, ...

BLOCK TRIANGULAR PRECONDITIONERS FOR -MATRICES AND MARKOV CHAINS MICHELE BENZI AND BORA UÇAR Abstract. We consider preconditioned Krylov subspace methods for solving large sparse linear systems under the assumption that the coefficient matrix is a (possibly singular) -matrix. The matrices are partitioned into block form using graph partitioning. Approximations to the Schur complement are used t...

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C∗-correspondence if and only if its fundamental relation R(A) is a tree admitting a Z+0 -valued continuous and coherent cocycle. For triangular limit algebras which are isomorphic to tensor algebras, we give a very concrete description for their defining C∗-correspondence and we show that it forms a complete in...

A set D subset of V(G) is a dominating graph G if for all x ϵ V(G)\D, some y such that xy E(G). called connected the subgraph <D> induced by connected. domination number G, denoted γ_c(G), minimum cardinality D. The triple repetition sequence {S_n:n Z+} positive integers which repeated thrice, i.e., {S_n}={1,1,1,2,2,2,3,3,3, ...}. In this paper, we construct combinatorial explicit formula...

Graphs have applications in all areas of science and therefore the interest Graph Theory is increasing everyday. They Chemistry, Pharmacology, Anthropology, Biology, Network Sciences etc. In this paper, theory connected with algebra by means a new graph invariant Ω define triangular graphs as degree sequence consisting n successive numbers use its properties to give characterization them. We co...

We define a new percolation model by generalising the FK representation of the Ising model, and show that on the triangular lattice and at high temperatures, the critical point in the new model corresponds to the Ising model. Since the new model can be viewed as Bernoulli percolation on a random graph, our result makes an explicit connection between Ising percolation and critical Bernoulli perc...