Related papers: Low dimensional strongly perfect lattices. I: The …

The Kodaira dimension of a nondegenerate toric hypersurface can be computed from the dimension of the Fine interior of its Newton polytope according to recent work of Victor Batyrev, where the Fine interior of the Newton polytope is the…

One possible way to obtain the quasicrystallographic structures is the projections of the higher dimensional lattices into 2D or 3D subspaces. In this work we introduce a general technique applicable to any higher dimensional lattice. We…

It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right…

In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…

Let p be a prime. We prove that there is an anti-equivalence between the category of unipotent strongly divisible lattices of weight p-1 and the category of Galois stable Z_p lattices in unipotent semi-stable representations with Hodge-Tate…

We present a mechanism which lifts a multiplicative lattice to a (weak) ideal system on some monoid.

Starting from a simple discrete model which exhibits a supersymmetric invariance we construct a local, interacting, two-dimensional Euclidean lattice theory which also admits an exact supersymmetry. This model is shown to correspond to the…

We study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a complete geometric description of the compact convex sets with…

Let \Lambda be a minimal Kac-Moody group of rank 2 defined over the finite field F_q, where q = p^a with p prime. Let G be the topological Kac-Moody group obtained by completing \Lambda. An example is G=SL_2(K), where K is the field of…

For a positive integer $s$, a lattice $L$ is said to be $s$-integrable if $\sqrt{s}\cdot L$ is isometric to a sublattice of $\mathbb{Z}^n$ for some integer $n$. Conway and Sloane found two minimal non $2$-integrable lattices of rank $12$…

In an earlier paper (math.NT/9906019) we showed that any integral unimodular lattice L of rank n which is not isometric with Z^n has a characteristic vector of norm at most n-8. [A "characteristic vector" of L is a vector w in L such that…

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d…

In this short note we give a construction of an infinite series of Delone simplices whose relative volume grows super-exponentially with their dimension. This dramatically improves the previous best lower bound, which was linear.

Let G be a topological Kac-Moody group of rank 2 with symmetric Cartan matrix, defined over a finite field F_q. An example is G = SL(2,F_q((t^{-1}))). We determine a positive lower bound on the covolumes of cocompact lattices in G, and…

We prove sharp upper bounds on the volume and the number of lattice points on edges of higher-dimensional reflexive simplices. These convex-geometric results are derived from new number-theoretic bounds on the denominators of unit fractions…

This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…

We give a new existence proof for the rank 2^d even lattices usually called the Barnes-Wall lattices, and establish new results on uniqueness, structure and transitivity of the automorphism group on certain kinds of sublattices. Our proofs…

We prove that if $\Gamma$ is a lattice in a classical simple Lie group $G$, then the symmetric space of $G$ is $\Gamma$-equivariantly homotopy equivalent to a proper cocompact $\Gamma$-CW complex of dimension the virtual cohomological…

A Type II lattice of norm 8 in dimension 72 is obtained by Construction A applied to an extended Quadratic Residue code over Z8. Its automorphism group contains a subgroup isomorphic to PSL(2,71).

The two-dimensional quantum lattice Toda model for the affine and simple Lie algebras of the type A is considered. For its known L-operator a correction of the second order in the lattice parameter is found. It is proved that the equation…