Related papers: Weak group inverse

We present a new class of sparse and easily invertible circulant matrices that can have a sparse inverse though not being permutation matrices. Their study is useful in the design of quasi-cyclic low-density generator matrix codes, that are…

We introduce a preorder on an inverse semigroup $S$ associated to any normal inverse subsemigroup $N$, that lies between the natural partial order and Green's ${\mathscr J}$-relation. The corresponding equivalence relation $\simeq_N$ is not…

We consider the problem of joint estimation of structured inverse covariance matrices. We perform the estimation using groups of measurements with different covariances of the same unknown structure. Assuming the inverse covariances to span…

We determine the structure of the bigraded ring of weak Jacobi forms with integral Fourier coefficients. This ring is the target ring of a map generalising the Witten and elliptic genera and a partition function of $(0,2)$-model in string…

The aim of this work is to extend to finite potent endomorphisms the notion of G-Drazin inverse of a finite square matrix. Accordingly, we determine the structure and the properties of a G-Drazin inverse of a finite potent endomorphism and,…

Using the tools of reverse mathematics in second-order arithmetic, as developed by Friedman, Simpson, and others, we determine the axioms necessary to develop various topics in commutative ring theory. Our main contributions to the field…

Permutation polynomials and their compositional inverses have wide applications in cryptography, coding theory, and combinatorial designs. Motivated by several previous results on finding compositional inverses of permutation polynomials of…

The notion of the core inverse of tensors with the Einstein product was introduced, very recently. This paper we establish some sufficient and necessary conditions for reverse-order law of this inverse. Further, we present new results…

We present explicit formulas for Moore-Penrose inverses of some families of set inclusion matrices arising from sets, vector spaces, and designs.

We introduce a new class of fractional backward orthogonal functions designed for the spectral approximation of weakly singular adjoint Volterra integral equations. These basis functions generate an approximation space that naturally…

In quantum theory, a weak value is a complex number with a somewhat technical definition: it is a ratio whose numerator is the matrix element of a self-adjoint operator and whose denominator is the inner product of a corresponding pair of…

In this paper, the index groups for which the weighted Young's inequalities hold in both continuous case and discrete case are characterized. As applications, the index groups for the product inequalities on modulation spaces are…

We generalize the notion of weakly mixing unitary representations to locally compact quantum groups, introducing suitable extensions of all standard characterizations of weak mixing to this setting. These results are used to complement the…

In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular…

A weakly equivariant Hopf algebra is a Hopf algebra A with an action of a finite group G up to inner automorphisms. We show that each weakly equivariant Hopf algebra can be replaced by a Morita equivalent algebra B with a strict action of G…

Ordering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has…

The notions of weakly bipartitive and bipartitive families were introduced by Montgolfier (2003) as a general tool for studying some decomposition of graphs and other combinatorial structures. In this paper, we give a matrix description of…

In this note we give a precise statement and a detailed proof for reconstruction problem of weak bialgebra maps. As an application we characterize indecomposability of weak algebras in categorical setting.

In this paper we consider the rank generating function of a separable permutation $\pi$ in the weak Bruhat order on the two intervals $[\text{id}, \pi]$ and $[\pi, w_0]$, where $w_0 = n,(n-1),..., 1$. We show a surprising result that the…

We give an algebraic characterisation of ordered groupoids, namely, we show that there is a categorical isomophism between the category of ordered groupoids and the category of $D$-inverse constellations. Here constellations are partial…