Related papers: Pascal Pyramids, Pascal Hyper-Pyramids and a Bilat…
A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizeable; that is, if all 2-generated subalgebras are…
The duality triads were defined in the preceding paper.(ArXiv: math.GM/0402260 v 1 Feb. 2004). Notation, enumeration of formulas and references is therefore to be continued hereby. In this paper Fibonomial triangle and further Pascal-like…
The three anti-commutative two-dimensional Pauli Pascal triangles can be generalized into multi-dimensional Pauli Pascal hyperpyramids. Fibonacci and Jacobsthal numbers are then generalized into Pauli Fibonacci numbers, Pauli Jacobsthal…
The massive topologically and self dual theories en seven dimensions are considered. The local duality between these theories is established and the dimensional reduction lead to the different dualities for massive antisymmetric fields in…
We give a generalization of the Pascal triangle called the quasi s-Pascal triangle where the sum of the elements crossing the diagonal rays produce the s-bonacci sequence. For this, consider a lattice path in the plane whose step set is {L…
Recently, a new generalization of Pascal's triangle, the so-called hyperbolic Pascal triangles were introduced. The mathematical background goes back to the regular mosaics in the hyperbolic plane. In this article, we investigate the paths…
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades:…
Bisymmetric Macdonald polynomials can be obtained through a process of antisymmetrization and $t$-symmetrization of non-symmetric Macdonald polynomials. Using the double affine Hecke algebra, we show that the evaluation of the bisymmetric…
Planar linkages are a rich area of study motivated by practical applications in engineering mechanisms. A central result is Kempe's Universality Theorem, which states that semi-algebraic sets can be realized by planar linkages. Polyhedral…
Certain topics on polygons are extended from Euclidean to hyperbolic geometry. This first part deals with uniqueness and existence of cocyclic polygons with prescribed sidelengths. The non-Euclidean versions are more difficult due to the…
With every family of finitely many subsets of a finite-dimensional vector space over the Galois-field with two elements we associate a cyclic transversal polytope. It turns out that those polytopes generalize several well-known polytopes…
We define twisted Alexander polynomials of a complex hypersurface with arbitrary singularities. These generalize the classical Alexander polynomials of high dimensional hypersurfaces and the twisted Alexander polynomial of plane curves. We…
Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain Diophantine equations. We look at a number of such questions including the question of approximating arbitrary…
We introduce a new class of division algebras, the hyperpolyadic algebras, which correspond to the binary division algebras $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{O}$ without considering new elements. First, we use the matrix…
General structure of the multivariate plain and q-hypergeometric terms and univariate elliptic hypergeometric terms is described. Some explicit examples of the totally elliptic hypergeometric terms leading to multidimensional integrals on…
Parabolic bifurcations in one complex dimension demonstrate a wide variety of interesting dynamical phenomena. In this paper we consider parabolic bifurcations of families of diffeomorphisms in two complex dimensions. Specifically we…
Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.
The classic way to write down Pascal's triangle leads to entries in alternating rows being vertically aligned. In this paper, we prove a linear dependence on vertically aligned entries in Pascal's triangle. Furthermore, we give an…
The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…
This work is divided into three parts. The first part concerns polynomials in one variable with all real roots. We consider linear transformations that preserve real rootedness, as well as matrices that preserve interlacing. The second part…