Related papers: Cubes of symmetric designs
Cubical rectangles are being defined and explored here over the $n-$dimensional geometric cube $Q_n.$ They form a new class of geometric objects that includes all the edges and all the squares of the $n-$cube. We enumerate and characterize…
We define and investigate a new three-parameter family of graphs that further generalizes the Fibonacci and metallic cubes. Namely, the number of vertices in this family of graphs satisfies Horadam recurrence, a linear recurrence of second…
An incidence structure consists simply of a set P of points and a set B of blocks, with a relation of incidence between points and blocks.A symmetric (v,k,\lambda) block design is the subject of this paper. The symmetric (n^2+n+1, n+1,1)…
Hadamard matrices are $(-1, +1)$ square matrices with mutually orthogonal rows. The Hadamard conjecture states that Hadamard matrices of order $n$ exist whenever $n$ is $1$, $2$, or a multiple of $4$. However, no construction is known that…
A new family of asymmetric matrices of Walsh-Hadamard type is introduced. We study their properties and, in particular, compute their determinants and discuss their eigenvalues. The invertibility of these matrices implies that certain…
In this paper we introduce a switching for 2-designs. We illustrate this method by applying it to some symmetric (64,28,12) designs. In that way we obtain six new symmetric (64,28,12) designs. Further, we show that this type of switching…
Associated to any finite metric space are a large number of objects and quantities which provide some degree of structural or geometric information about the space. In this paper we show that in the setting of subsets of weighted Hamming…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
A linked system of symmetric designs (LSSD) is a $w$-partite graph ($w\geq 2$) where the incidence between any two parts corresponds to a symmetric design and the designs arising from three parts are related. The original construction for…
We consider the structure of the point-line incidence matrix of the projective space $\mathrm{PG}(3,q)$ connected with orbits of points and lines under the stabilizer group of the twisted cubic. Structures of submatrices with incidences…
A Hadamard matrix is a scaled orthogonal matrix with $\pm 1$ entries. Such matrices exist in certain dimensions: the Hadamard conjecture is that such a matrix always exists when $n$ is a multiple of 4. A conjecture attributed to Ryser is…
A $n\times n$ matrix $A$ has normal defect one if it is not normal, however can be embedded as a north-western block into a normal matrix of size $(n+1)\times (n+1)$. The latter is called a minimal normal completion of $A$. A construction…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
The paper studies the interpolation properties of net spaces $N_{p,q}(M)$, when $M$ is the set of dyadic cubes in $\mathbb{R}^n$, and also when $M$ is the family of all cubes with parallel faces to the coordinate axes in $\mathbb{R}^n$. It…
A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…
Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the…
The notion of unbiased orthogonal designs is introduced as a generalization among unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several constructions for mutually…
We consider the structure of the plane-line incidence matrix of the projective space $\mathrm{PG}(3,q)$ with respect to the orbits of planes and lines under the stabilizer group of the twisted cubic. Structures of submatrices with…
Classification of N=4 superconformal symmetries in two dimensions is re-examined. It is proposed that apart from SU(2) and $SU(2)\times SU(2)\times U(1)$ their Kac-Moody symmetry can also be $SU(2)\times(U(1))^4$. These superconformal…