Related papers: Symmetries in generalized Kaprekar routine

In this work, we introduce a symmetric algorithm obtained by the recurrence relation a_{n}^{k}=a_{n-1}^{k}+a_{n}^{k-1}. We point out that this algorithm can be apply to hyperharmonic-, ordinary and incomplete Fibonacci- and Lucas numbers.…

The computation of the normaliser of a permutation group in the full symmetric group is an important and hard problem in computational group theory. This article reports on an algorithm that builds a descending chain of overgroups to…

An extension of the finite and infinite Lie groups properties of complex numbers and functions of complex variable is proposed. This extension is performed exploiting hypercomplex number systems that follow the elementary algebra rules. In…

Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…

The coefficients appearing at leading and subleading order in the $1/m$ expansion of bilinear heavy quark currents are related to each other by imposing reparametrization invariance on both the effective current operators and the…

We consider the problem of learning regression functions from pairwise data when there exists prior knowledge that the relation to be learned is symmetric or anti-symmetric. Such prior knowledge is commonly enforced by symmetrizing or…

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine…

We study a positive-definite function associated to a measure-preserving equivalence relation on a standard probability space and use it to measure quantitatively the proximity of subequivalence relations. This is combined with a recent…

In the context of Hecke algebras of complex reflection groups, we prove that the generalized Hecke algebras of normalizers of parabolic subgroups are semidirect products, under suitable conditions on the parameters involved in their…

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…

We describe those group algebras over fields of characteristic different from 2 whose units symmetric with respect to the classical involution, satisfy some group identity.

Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor…

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by…

The similarity transformations of quantum orthogonal groups are developed and FRT theory is reformulated to the Cartesian basis. The quantum orthogonal Cayley-Klein groups are introduced as the algebra functions over an associative algebra…

We study invariance properties of Colombeau generalized functions under actions of smooth Lie transformation groups. Several characterization results analogous to the smooth setting are derived and applications to generalized rotational…

It is believed that some numerical technique must be employed for the determination of the system parameters of a visual binary or a star with a planet because the relevant equations are not only highly nonlinear but also transcendental…

We introduce a new notion of "regularity structure" that provides an algebraic framework allowing to describe functions and / or distributions via a kind of "jet" or local Taylor expansion around each point. The main novel idea is to…

For an affine Lie algebra $\hat{\mathfrak g}$ the coefficients of certain vertex operators which annihilate level $k$ standard $\hat{\mathfrak g}$-modules are the defining relations for level $k$ standard modules. In the paper \cite{PS3}…

To an ergodic, essentially free and measure-preserving action of a non-amenable Baumslag-Solitar group on a standard probability space, a flow is associated. The isomorphism class of the flow is shown to be an invariant of such actions of…

In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…