Related papers: Pauli matrices and ring puzzles

Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

In the present paper we show that it is possible to obtain the well known Pauli group $P=\langle X,Y,Z \ | \ X^2=Y^2=Z^2=1, (YZ)^4=(ZX)^4=(XY)^4=1 \rangle $ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of…

We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.

We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…

In this paper, on envelopes created by circle families in the plane, all four basic problems (existence problem, representation problem, problem on the number of envelopes, problem on relationships of definitions) are solved.

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a…

In this paper we consider a general sequence of orthogonal Laurent polynomials on the unit circle and we first study the equivalences between recurrences for such families and Szego's recursion and the structure of the matrix representation…

We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…

We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.

The study of partial-twuality polynomials originates from the classical operations of geometric duality and Petrie duality on cellularly embedded graphs. These involutions generate the symmetric group $S_3$, and applying them to subsets of…

We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

We construct a moduli space for the connected subgroups of an algebraic group and the corresponding universal family. Morphisms from an algebraic variety to this moduli space correspond to flat families of connected algebraic subgroups…

The conjugation action of the complex orthogonal group on the polynomial functions on $n \times n$ matrices gives rise to a graded algebra of invariant polynomials. A spanning set of this algebra is in bijective correspondence to a set of…

We study a geometric property related to spherical hyperplane tessellations in $\mathbb{R}^{d}$. We first consider a fixed $x$ on the Euclidean sphere and tessellations with $M \gg d$ hyperplanes passing through the origin having normal…

We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…

In the Euclidean plane ${\bf{E}}^2$, fix four pairwise distinct points \begin{equation*} \label{eqA} \begin{array}{ccc} A=(a_1,a_2),\ B=(b_1,b_2),\ C=(c_1,c_2),\ D=(d_1,d_2), \end{array} \end{equation*} together with four non-zero real…