Related papers: Classification of positive definite lattices

In this paper, we introduce and study the Dirichlet series enumerating (proper) equivalence classes of full rank subforms/sublattices of a given quadratic form/lattice, focusing on the positive definite binary case. We obtain formulas…

Let L be a positive definite even lattice and V_L^+ be the fixed points of the lattice VOA V_L associated to L under an automorphism of V_L lifting the -1 isometry of L. For any positive rank, the full automotphism group of V_L^+ is…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

The methods to classify extremal unimodular lattices with given automorphisms are extended to the situation of modular lattices. A slightly more general notion than the type from the PhD thesis of Michael Juergens is the det-type. The…

We classify the unimodular equivalence classes of inclusion-minimal polygons with a certain fixed lattice width. As a corollary, we find a sharp upper bound on the number of lattice points of these minimal polygons.

The classification of reflective modular forms is an important problem in the theory of automorphic forms on orthogonal groups. In this paper, we develop an approach based on the theory of Jacobi forms to give a full classification of…

This article is based upon previous work by Sousa Ramos and his collaborators. They first prove that the existence of only one orbit associated with the Collatz conjecture is equivalent to the determinant of each matrix of a certain…

We classified finite orbits of monodromies of the Fuchsian system for five $2\times 2$ matrices. The explicit proof of this result is given. We have proposed a conjecture for a similar classification for $6$ or more $2\times 2$ matrices.…

We exhibit an explicit, deterministic algorithm for finding a canonical form for a positive definite matrix under unimodular integral transformations. We use characteristic sets of short vectors and partition-backtracking graph software.…

We present a classification of non-hermitian random matrices based on implementing commuting discrete symmetries. It contains 38 classes. This generalizes the classification of hermitian random matrices due to Altland-Zirnbauer and it also…

In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier lattice we attach a finite group by considering a naturally…

We classify and expose all the gradient Ricci solitons on complete surfaces, open or closed, with curvature bounded below, and possibly with a discrete set of cone-like singular points that arise naturally. We give a precise qualitative…

We prove an asymptotic formula for the number of fixed rank matrices with integer coefficients over a number field K/Q and bounded norm. As an application, we derive an approximate Rogers integral formula for discrete sets of module…

Characteristic Lie rings for Toda type 2+1 dimensional lattices are defined. Some properties of these rings are studied. Infinite sequence of special kind modules are introduced. It is proved that for known integrable lattices these modules…

We restate a process presented by Stanley as a technique to prove that there exists exactly one $d$-differential distributive lattice for any positive integer $d$. This process can be trivially extended to apply to distributive finitary…

We classify closed, conformally flat Lorentzian manifolds of dimension $n \geq 3$ with unipotent holonomy in PO(2,n). They are all Kleinian and fall into four different geometric types according to the intersection of the image of the…

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 discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…

In this article we study and obtain a classification of Ising vectors in vertex operator algebras associated to binary codes and $\sqrt{2}$ times root lattices, where an Ising vector is a conformal vector with central charge 1/2 generating…

We consider the set of all linear combinations with integer coefficients of the vectors of a unit tight equiangular $(k,n)$ frame and are interested in the question whether this set is a lattice, that is, a discrete additive subgroup of the…