Related papers: On the representability of totally unimodular matr…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters,…
We describe an infinite family of edge-decompositions of complete graphs into two graphs, each of which triangulate the same orientable surface. Previously, such decompositions had only been known for only a few complete graphs. These…
Let $EX[M_1\dots, M_k]$ denote the class of binary matroids with no minors isomorphic to $M_1, \dots, M_k$. In this paper we give a decomposition theorem for $EX[S_{10}, S_{10}^*]$, where $S_{10}$ is a certain 10-element rank-4 matroid. As…
A uniqueness theorem for an LU decomposition of a totally nonnegative matrix is obtained.
In this paper, we introduce the notion of a BCK-topological module in a natural way and establish that every decreasing sequence of submodules on a BCK-module M over bounded commutative BCK-algebra X is indeed a BCK- topological module. We…
A vertex in a graph dominates itself and each of its adjacent vertices. The \emph{$k$-tuple domination problem}, for a fixed positive integer $k$, is to find a minimum sized vertex subset in a given graph such that every vertex is dominated…
We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…
We prove the decomposition of arbitrary diagonal operators into tensor and matrix products of smaller matrices, focusing on the analytic structure of the resulting formulas and their inherent symmetries. Diagrammatic representations are…
We give an exact algorithm to calculate (under some GKM-restriction) the matrix describing the embedding $\B(\s)_x\subset\B(\s)^x$, where the first module is the costalk and the second one is the stalk at $x$ of a Bott-Samelson module…
We prove that a large family of graphs which are decomposable with respect to the modular decomposition can be reconstructed from their collection of vertex-deleted subgraphs.
Let $R$ be a ring and let $\mathcal C$ be a small class of right $R$-modules which is closed under finite direct sums, direct summands, and isomorphisms. Let $\mathcal V (\mathcal C)$ denote a set of representatives of isomorphism classes…
The modular decomposition of a graph $G$ is a natural construction to capture key features of $G$ in terms of a labeled tree $(T,t)$ whose vertices are labeled as "series" ($1$), "parallel" ($0$) or "prime". However, full information of $G$…
Tensor train (TT) decomposition is a powerful representation for high-order tensors, which has been successfully applied to various machine learning tasks in recent years. However, since the tensor product is not commutative, permutation of…
The present paper deals with the discrete inverse problem of reconstructing binary matrices from their row and column sums under additional constraints on the number and pattern of entries in specified minors. While the classical…
Many "good" topologies for interconnection networks are based on line digraphs of regular digraphs. These digraphs support unitary matrices. We propose the property "being the digraph of a unitary matrix" as additional criterion for the…
Bidiagonal matrices are widespread in numerical linear algebra, not least because of their use in the standard algorithm for computing the singular value decomposition and their appearance as LU factors of tridiagonal matrices. We show that…
Let X, Y, and Z be topological modules over a topological ring R. In this paper, we introduce three different classes of bounded bigroup homomorphisms from X \times Y into Z with respect to the three different uniform convergence…
A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial…
An $n\times n$ complex matrix $M$ with entries in the $k^{\textrm{th}}$ roots of unity which satisfies $MM^{\ast} = nI_{n}$ is called a Butson Hadamard matrix. While a matrix with entries in the $k^{\textrm{th}}$ roots typically does not…
We diagonalize the $B$-element of monodromy matrix for noncompact open $SL(2,\mathbb{C})$ spin chain with boundary interaction. The monodromy matrix is defined in terms of $SL(2,\mathbb{C})$ $L$-operator and boundary $K$-matrix. The…