Related papers: A construction of spherical 3-designs

The fundamental Davis-Januszkiewicz construction of toric manifolds is reinterpreted in order to allow for generalization. Applications involve the simplicial wedge $J$-construction and Ayzenberg's recent identities arising from composed…

The rotational invariants constructed by the products of three spherical harmonic polynomials are expressed generally as homogeneous polynomials with respect to the three coordinate vectors, where the coefficients are calculated explicitly…

The present paper gives two concrete formulas for the volume of an arbitrary spherical tetrahedron, which is in a 3-dimensional spherical space of constant curvature +1. One formula is given in terms of dihedral angles, and another one is…

V. Bondarenko and Y. Drozd gives a description of all indecomposable objects in a category of representations of posets, nowadays known as the Bondarenko's category. This category was essential for V. Bekkert and H. Merklen classify all…

Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.

The computation of the effect of a simple monodromy defect in the case of a sphere with twisted boundary conditions is revisited and streamlined using earlier calculations for a similar system. Compact and explicit expressions are found for…

Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask…

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

An integral lattice which is generated by some vectors of norm $q$ is called $q$-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices…

In this paper we develop a concrete way to construct bodies of constant width in dimension three. They are constructed from special embeddings of self-dual graphs.

In 1963, Shrikhande and Raghavarao published a recursive construction for designs that starts with a resolvable design (the "master design") and then uses a second design (the "indexing design") to take certain unions of blocks in each…

The purpose of this paper is to give an effective construction for some induced structures on spheres or product of spheres of codimension 1, 2 or 3, respectively, in Euclidean space endowed with an almost product structure.

Building on a classical solution to the pentagon equation, constructed earlier by the author and E.V. Martyushev and related to the flat geometry invariant under the group SL(2), we construct an algebraic complex corresponding to a…

We give a geometric construction of the three infinite series of K3 surfaces which are sandwiched by Kummer surfaces within a Shioda-Inose structure. Explicit examples are also provided.

We give a combinatorial description of general homotopy groups of $k$-dimensional spheres with $k\geq3$ as well as those of Moore spaces. For $n>k\geq 3,$ we construct a finitely generated group defined by explicit generators and relations,…

We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a question of Cameron. We also arrive at a natural description of all…

By examining arithmetic operations between decimal numbers in a given base m we uncover fractal structures that generalize the Sierpinski triangle

We describe the construction of the slice fibration of a given one.

We provide an illustration of a geometric structure that exhibits the spin-half wave-function characteristics, namely that its full rotation displays a phase inversion. We show that general fractional-spin geometric structures are possible,…

Based on a simple example, quantization of some 3-spaces is explained.