Related papers: The quasi principal rank characteristic sequence

The aim of this work is a systematic investigation of the possible parameters of quasi-perfect (QP) binary and ternary linear codes of small dimensions and preparing a complete classification of all such codes. First we give a list of…

A minimal (by inclusion) generating set for the algebra of semi-invariants of a quiver of dimension (2,...,2) is established over an infinite field of arbitrary characteristic. The mentioned generating set consists of the determinants of…

Chung and Graham define quasirandom subsets of $\mathbb{Z}_n$ to be those with any one of a large collection of equivalent random-like properties. We weaken their definition and call a subset of $\mathbb{Z}_n$ $\epsilon$-balanced if its…

A simple criterion is derived in order that a number sequence ${\cal S}_n$ is a permitted spectrum of a quantized system. The sequence of the prime numbers fulfils the criterion and the corresponding one-dimensional quantum potential is…

We show that every quasitrivial n-ary semigroup is reducible to a binary semigroup, and we provide necessary and sufficient conditions for such a reduction to be unique. These results are then refined in the case of symmetric n-ary…

There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…

Transforming an asymmetric system into a symmetric system makes it possible to exploit the simplifying properties of symmetry in control problems. We define and characterize the family of symmetrizable systems, which can be transformed into…

The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of the largest square submatrix with nonzero permanent is defined…

Building on the classification of all characteristic polynomials of integer symmetric matrices having small span (span less than 4), we obtain a classification of small-span polynomials that are the characteristic polynomial of a Hermitian…

A characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over other characteristics. In this…

We show how to obtain linear combinations of polynomials in an orthogonal sequence $\{P_n\}_{n\geq 0}$, such as $Q_{n,k}(x)=\sum\limits_{i=0}^k a_{n,i}P_{n-i}(x)$, $a_{n,0}a_{n,k}\neq0$, that characterize quasi-orthogonal polynomials of…

We provide a description of the class of n-ary operations on an arbitrary chain that are quasitrivial, symmetric, nondecreasing, and associative. We also prove that associativity can be replaced with bisymmetry in the definition of this…

A mixed quasi-\'etale quotient is the quotient of the product of a curve of genus at least 2 with itself by the action of a group which exchanges the two factors and acts freely out of a finite subset. A mixed quasi-\'etale surface is the…

Sylvester's criterion characterizes positive definite (PD) and positive semidefinite (PSD) matrices without the need of eigendecomposition. It states that a symmetric matrix is PD if and only if all of its leading principal minors are…

An independent vertex subset $S$ of the directed graph $G$ is a kernel if the set of out-neighbors of $S$ is $V(G)\setminus S$. An independent vertex subset $Q$ of $G$ is a quasi-kernel if the union of the first and second out-neighbors…

We study the point pair function in subdomains $G$ of $\mathbb{R}^n$. We prove that, for every domain $G\subsetneq\mathbb{R}^n$, the this function is a quasi-metric with the constant less than or equal to $\sqrt{5}\slash2$. Moreover, we…

A real square matrix is Perron-like if it has a real eigenvalue $s$, called the principal eigenvalue of the matrix, and $\mbox{Re}\,\mu<s$ for any other eigenvalue $\mu$. Nonnegative matrices and symmetric ones are typical examples of this…

Chebotarev's theorem on roots of unity states that all minors of a Fourier matrix are non-zero if and only if the order of the matrix is prime. We establish cases in which all principal minors of Fourier matrices of square-free order are…

We study the differential and metric structures of the set of real square roots of a non-singular real matrix, under the assumption that the matrix and its square roots are semi-simple, or symmetric, or orthogonal.

A (Hasse) diagram of a finite partially ordered set (poset) P will be called quasiplanar if for any two incomparable elements u and v, either v is on the left of all maximal chains containing u, or v is on the right of all these chains.…