Related papers: Matrices with cyclically monotone rows and Cantor …
The number of non-negative integer matrices with given row and column sums appears in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations of various kinds. Here we…
An alternating sign matrix is a square matrix satisfying (i) all entries are equal to 1, -1 or 0; (ii) every row and column has sum 1; (iii) in every row and column the non-zero entries alternate in sign. The 8-element group of symmetries…
In \cite{M18}, the first author gave a construction of strongly regular Cayley graphs on the additive group of finite fields by using three-valued Gauss periods. In particular, together with the result in \cite{BLMX}, it was shown that…
A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miyano, and Ueno states that a matroid M is cyclically…
Given a parity-check matrix $H_m$ of a $q$-ary Hamming code, we consider a partition of the columns into two subsets. Then, we consider the two codes that have these submatrices as parity-check matrices. We say that anyone of these two…
Many combinatorial matrices --- such as those of binomial coefficients, Stirling numbers of both kinds, and Lah numbers --- are known to be totally non-negative, meaning that all minors (determinants of square submatrices) are non-negative.…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We examine the noncommutative cylinder solution to a matrix model with a Minkowski background metric. It can be regarded as the noncommutative analogue of a static circular string. Perturbations about the solution yield a tachyonic scalar…
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory,…
We extend classical results of Rado on partition regularity of systems of linear equations with integer coefficients to the case when the coefficient ring is either an arbitrary integral domain or a noetherian ring. In particular, we show…
Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized…
In this paper, we study convolutional codes with a specific cyclic structure. By definition, these codes are left ideals in a certain skew polynomial ring. Using that the skew polynomial ring is isomorphic to a matrix ring we can describe…
The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. We show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix…
Understanding the structure of the fermion mixing matrices is an important question in particle physics. The quark mixing matrix is approximately diagonal while the lepton mixing matrix has large off-diagonal elements. Attempting to…
The M-matrix is an important concept in matrix theory, and has many applications. Recently, this concept has been extended to higher order tensors [18]. In this paper, we establish some important properties of M-tensors and nonsingular…
It is well known that square matrices with independent and identically distributed (iid) random entries are typically well conditioned. A natural question is whether this favorable behavior persists for random matrices whose entries obey…
We prove existence of small amplitude, $2\pi \slash \om$-periodic in time solutions of completely resonant nonlinear wave equations with Dirichlet boundary conditions, for any frequency $ \om $ belonging to a Cantor-like set of positive…
The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by a positive Cantor series are formulated for the case of an…
A combinatorial rectangle may be viewed as a matrix whose entries are all +-1. The discrepancy of an m by n matrix is the maximum among the absolute values of its m row sums and n column sums. In this paper, we investigate combinatorial…
For a matroid $M$, an element $e$ such that both $M\backslash e$ and $M/e$ are regular is called a regular element of $M$. We determine completely the structure of non-regular matroids with at least two regular elements. Besides four small…