Related papers: A new Euclidean tight 6-design

We improve the best lower bounds on the chromatic number of Euclidean space in small dimensions. The new results depend on extensive computations in Sage.

This article introduces a new approach to discrete curvature based on the concept of effective resistances. We propose a curvature on the nodes and links of a graph and present the evidence for their interpretation as a curvature. Notably,…

Let F be a finite field and G=GL(6,F). In this paper, we explicitly describe a certain twisted Jacquet module of an irreducible cuspidal representation of G.

We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six.

We prove several structural properties of Steiner triple systems (STS) of order 3w+3 that include one or more transversal subdesigns TD(3,w). Using an exhaustive search, we find that there are 2004720 isomorphism classes of STS(21)…

A Euclidean $t$-design, as introduced by Neumaier and Seidel (1988), is a finite set ${\cal X} \subset \mathbb{R}^n$ with a weight function $w: {\cal X} \rightarrow \mathbb{R}^+$ for which $$\sum_{r \in R} W_r \overline{f}_{S_{r}} =…

We present an new system of ordinary differential equations with affine Weyl group symmetry of type E_6^{(1)}. This system is expressed as a Hamiltonian system of sixth order with a coupled Painleve VI Hamiltonian.

In this paper, we study spherical $T$-designs and their harmonic strength $\text{Hst}(X)$ on the unit circle $S^1$. For any finite set $T\subset\mathbb{N}$, we constructively demonstrate the existence of a finite design $X$ such that…

We show how recent exact results in supersymmetric theories can be extended to models which include {\it explicit} soft supersymmetry breaking terms. We thus derive new exact results for non-supersymmetric models.

We classify the possible torsion structures of rational elliptic curves over sextic number fields.

We re-derive the R symmetries for the Z6-II orbifold with non-trivial Wilson lines and find expressions for the R charges which differ from those in the literature.

We give a new proof of the existence of designs, which is much shorter and gives better bounds.

A five dimensional $SU(6)$ grand gauge-Higgs unification compactified on $S^1/Z_2$ is discussed. We propose new sets of the $SU(6)$ representations where the quarks and leptons in one generation are embedded and there is no extra massless…

We obtain some new inequalities of Chebyshev Type.

We prove elegant trilinear formulas connecting products of volumes of Euclidean tetrahedra with vertices taken from a given set of 6 points. We propose a way for generalizing those formulas.

We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.

The proof of Dey's new k-set bound is illustrated.

We extend our previous work by building a smooth complete manifold $(M^6,g,p)$ with $\mathrm{Ric}\geq 0$ and whose fundamental group $\pi_1(M^6)=\mathbb{Q}/\mathbb{Z}$ is infinitely generated. The example is built with a variety of…

We study the examples mentioned in [2,Tables A & C] and establish the arithmeticity of four examples of symplectic hypergeometric groups of degree six. Following [2] we know that there are 458 inequivalent symplectic hypergeometric groups…

The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised $_6\phi_5$ series.