Related papers: Some new Steiner designs $S(2,6,91)$

We revisit the configuration of Danzer DCD(4), a great inspiration for our work. This configuration of type (35_4) falls into an infinite series of geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by…

Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…

Unitary $t$-designs are `good' finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many…

In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…

The inverse problem of designing component interactions to target emergent structure is fundamental to numerous applications in biotechnology, materials science, and statistical physics. Equally important is the inverse problem of designing…

Factorization method is developed for a family of discretely spiked harmonic oscillators. Two sets of intertwining and ladder operators are presented to algebraically generate eigenstates with energies isomorphic to those of the ordinary…

A maximal subgroup of the Mathieu group M24 arises as the combined holomorphic symplectic automorphism group of all Kummer surfaces whose Kaehler class is induced from the underlying complex torus. As a subgroup of M24, this group is the…

A long standing problem is the supergauge completion of AdS_4 x (G/H)_7 or AdS_5 x (G/H)_5 backgrounds which preserve less then maximal supersymmetry. In parallel with the supersolvable realization of the AdS_4 x S^7 background based on…

Several methods for generating random Steiner triple systems (STSs) have been proposed in the literature, such as Stinson's hill-climbing algorithm and Cameron's algorithm, but these are not yet completely understood. Those algorithms, as…

General Schr\"{o}dinger equation is considered with a central polynomial potential depending on $2q$ arbitrary coupling constants. Its exceptional solutions of the so called Magyari type (i.e., exact bound states proportional to a…

We show that for any n divisible by 3, almost all order-n Steiner triple systems admit a decomposition of almost all their triples into disjoint perfect matchings (that is, almost all Steiner triple systems are almost resolvable).

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…

We give an algebraic and a geometric criterion for the existence of $G$-connections on $\mathbb{P}^{1}$ with prescribed irregular type with equal slope at $\infty$ (isoclinic) and with regular singularity of prescribed residue at $0$. The…

Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace…

Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing…

The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n=2^m-1 for small m, m < 23, is given. As far as we know, for m in {5,7,11,13,17,19}, all given…

One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a…

We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general 6-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite…

Group equivariant convolutional networks (GCNNs) endow classical convolutional networks with additional symmetry priors, which can lead to a considerably improved performance. Recent advances in the theoretical description of GCNNs revealed…

Iterative rounding has enjoyed tremendous success in elegantly resolving open questions regarding the approximability of problems dominated by covering constraints. Although iterative rounding methods have been applied to packing problems,…