Related papers: The quasi principal rank characteristic sequence
In this investigation of character tables of finite groups we study basic sets and associated representation theoretic data for complementary sets of conjugacy classes. For the symmetric groups we find unexpected properties of characters on…
Using techniques developed in \cite{KLR}, we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider are called {\em almost complete congruency…
Let n_d denote the degree d Veronese embedding of a projective space P^r. For any symmetric tensor P, the 'symmetric tensor rank' sr(P) is the minimal cardinality of a subset A of P^r, such that n_d(A) spans P. Let S(P) be the space of all…
A quasi-kernel of a digraph $D$ is an independent set $Q$ such that every vertex can reach $Q$ in at most two steps. A 48-year conjecture made by P.L. Erd\H{o}s and Sz\'ekely, denoted the small QK conjecture, says that every sink-free…
We study finite quasi-quantum groups in their quiver setting developed recently by the first author in arXiv:0902.1620 and arXiv:0903.1472. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation…
The problem of completing a large low rank matrix using a subset of revealed entries has received much attention in the last ten years. The main result of this paper gives a necessary and sufficient condition, stated in the language of…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
We address the question of the infinitude of twin and cousin prime pairs from a probabilistic perspective. Our approach partitions the set of integer numbers greater than $2$ in finite intervals of the form $[p_{n-1}^2,p_n^2)$, $p_{n-1}$…
Nowhere dense classes of graphs are very general classes of uniformly sparse graphs with several seemingly unrelated characterisations. From an algorithmic perspective, a characterisation of these classes in terms of uniform quasi-wideness,…
In this study, we introduce the notion of $PL_\delta$-homeomorphisms of $\mathbb{R}^n$. Furthermore, we provide a combinatorial criterion reliant on the vertices and edges of simplicial structures, to determine whether a piecewise-linear…
The relevant quasipotential near an equilibrium point is determined by a new linear matrix equation, with less unknowns than an existing (possibly nonlinear) one. This also assures the asymptotic fulfillment of the Fokker-Planck equation,…
We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…
It is proved that a system of parameters is always a Q-sequence for several classes of mixed characteristic rings: rings in which the characteristic of the residue field is a nilpotent element, a mixed characteristic analogue of…
The class of quasiseparable matrices is defined by a pair of bounds, called the quasiseparable orders, on the ranks of the maximal sub-matrices entirely located in their strictly lower and upper triangular parts. These arise naturally in…
We solve the Symmetrized Principal Minor Assignment Problem, that is we show how to determine if for a given vector $v\in \mathbb{C}^{n}$ there is an $n\times n$ matrix that has all $i\times i$ principal minors equal to $v_{i}$. We use a…
In this paper, the concept of quasi-finitely separating map and quasiapproximate identity are introduced. Based on these concepts, QFS-spaces and quasicontinuous maps are defined. Properties and characterizations of QFS-spaces are explored.…
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel matrix over F_q to be nonsingular.…
In this paper, the new concept of quasi-prime ideal is introduced which at the same time generalizes the `prime ideal' and `primary ideal' notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which…
The combined matrix is a very useful concept for many applications. Almost strictly sign regular (ASSR) matrices form an important structured class of matrices with two possible zero patterns, which are either type-I staircase or type-II…
A quasi-entropy is constructed for tensors averaged by a density function on $SO(3)$ using the log-determinant of a covariance matrix. It serves as a substitution of the entropy for tensors derived from a constrained minimization that…