Related papers: A Combinatorial Result on Block Matrices
The standard theorem for regular stochastic matrices is generalized to matrices with no sign restriction on the entries. The condition that column sums be equal to 1 is kept, but the regularity condition is replaced by a condition on the…
In this paper, we derive some necessary and sufficient solvability conditions for some systems of one sided coupled Sylvester-type real quaternion matrix equations in terms of ranks and generalized inverses of matrices. We also give the…
In this paper, we introduce the generating functions of partition sequences. Partition sequences have a one-to-one correspondence with partitions. Therefore, the generating function has no multiplicity and appears meaningless initially.…
Positive semidefinite matrices partitioned into a small number of Hermitian blocks have a remarkable property. Such a matrix may be written in a simple way from the sum of its diagonal blocks
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
We give one more proof of the fact that symplectic matrices over real and complex fields have determinant one. While this has already been proved many times, there has been lasting interest in finding an elementary proof. Our result is…
We consider some combinatorial problems on matrix polynomials over finite fields. Using results from control theory we give a proof of a result of Helmke, Jordan and Lieb on the number of linear unimodular matrix polynomials over a finite…
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…
In this paper, we define the combinatorial wall-crossing transformation and the generalized column regularization on partitions and prove that a certain composition of these two transformations has the same effect on the one-row partition…
Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\mathcal{A}$ as an invariant set. We first characterize…
Ferrers graphs and tables of partitions are treated as vectors. Matrix operations are used for simple proofs of identities concerning partitions. Interpreting partitions as vectors gives a possibility to generalize partitions on negative…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
We discuss a conjecture concerning the enumeration of nonsingular matrices over a finite field that are block companion and whose order is the maximum possible in the corresponding general linear group. A special case is proved using some…
This note describes a technique for generating large non-singular matrices with blocks of full rank. Our motivation to construct such matrices arises in the white-box implementation of cryptographic algorithms with S-boxes.
We say that a semigroup of matrices has a submultiplicative spectrum if the spectrum of the product of any two elements of the semigroup is contained in the product of the two spectra in question (as sets). In this note we explore an…
Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by…
In the framework of model-based clustering, a model, called multi-partitions clustering, allowing several latent class variables has been proposed. This model assumes that the distribution of the observed data can be factorized into several…
In alternating sign matrices the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry…
This paper is concerned with the factorization and equivalence problems of multivariate polynomial matrices. We present some new criteria for the existence of matrix factorizations for a class of multivariate polynomial matrices, and obtain…
An integer linear system is a set of inequalities with integer constraints. The solution graph of an integer linear system is an undirected graph defined on the set of feasible solutions to the integer linear system. In this graph, a pair…