Related papers: Pascal Pyramids, Pascal Hyper-Pyramids and a Bilat…
Generalizing previous constructions, we present a dual pair of decompositions of the complement of a link L into bipyramids, given any multi-crossing projection of L. When L is hyperbolic, this gives new upper bounds on the volume of L…
Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new…
We introduce a bulging triangle like the generalization of the Reuleaux triangle. We may be able to propose various ways to bulge a triangle, but this paper presents the way so that its vertices are the same as them of the original…
The bilateral binomial theorem with step width two gives a bilateral hypergeometric formula for 2H2(a, a+1/2; c, c+1/2; z).
A "Two-Spaceship Paradox" in special relativity is resolved and discussed. We demonstrate a nonstandard resolution to the "two-spaceship paradox" by explicit calculation using Generalized Principle of limiting 4-dimensional symmetry…
In previous work on Clebsch-Gordan coefficients, certain remarkable hexagonal arrays of integers are constructed that display behaviors found in Pascal's Triangle. We explain these behaviors further using the binomial transform and discrete…
A large class of supersymmetric quantum field theories, including all theories with $\mathcal{N} = 2$ supersymmetry in three dimensions and theories with $\mathcal{N} = 2$ supersymmetry in four dimensions, possess topological-holomorphic…
The symmetric Macdonald polynomials are able to be constructed out of the non-symmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their non-symmetric…
We derive some, seemingly new, curious additive relations in the Pascal triangle. They arise in summing up the numbers in the triangle along some vertical line up to some place.
A new pseudoclassical supersymmetrical model of a spinning particle in 2+1 dimensions is proposed. Different ways of its quantization are discussed. They all reproduce the minimal quantum theory of the particle.
Duality of curves is one of the important aspects of the ``classical'' algebraic geometry. In this paper, using this foundation, the duality of tropical polynomials is constructed to introduce the duality of Non-Archimedean curves. Using…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…
We extend the notion of triangle to "imaginary triangles" with complex valued sides and angles, and parametrize families of such triangles by plane algebraic curves. We study in detail families of triangles with two commensurable angles,…
The paper describes a new algorithm of construction of the nonlinear arithmetic triangle on the basis of numerical simulation and the binary system. It demonstrates that the numbers that fill the nonlinear arithmetic triangle may be…
We pose and answer several questions concerning the number of ways to fold a polygon to a polytope, and how many polytopes can be obtained from one polygon; and the analogous questions for unfolding polytopes to polygons. Our answers are,…
A new and easy way of deriving Gauss's Generalized Hypergeometric Theorem is presented by using the Bilateral Binomial Theorem.
The pursuit of quantum advantage in simulating many-body quantum systems on quantum computers has gained momentum with advancements in quantum hardware. This work focuses on leveraging the symmetry properties of these systems, particularly…
All bialgebra structures on twodimensional Galilei algebra are classified. The corresponding Lie-Poisson structures on Galilei group are found.
We consider three types of rings of supersymmetric polynomials: polynomial ones $\Lambda_{m,n}$, partially polynomial $\Lambda_{m,n}^{+y}$ and Laurent supersymmetric rings $\Lambda_{m,n}^{\pm}$. For each type of rings we give their…