Related papers: Unimodular Hunting II
A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…
A lattice L is slim if it is finite and the set of its join-irreducible elements contains no three-element antichain. Slim, semimodular lattices were previously characterized by G. Cz\'edli and E.T. Schmidt as the duals of the lattices…
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…
In this article, we present two methods to construct 2-uninorms on bounded lattices by using additive generators, which are further used for inducing uninorms, nullnorms, uni-nullnorms and null-uninorms, respectively. We also provide some…
In this paper, all irreducible weight modules with finite dimensional weight spaces over the twisted Heisenberg-Virasoro algebra are determined. There are two different classes of them. One class is formed by simple modules of intermediate…
We study lattices in non-positively curved metric spaces. Borel density is established in that setting as well as a form of Mostow rigidity. A converse to the flat torus theorem is provided. Geometric arithmeticity results are obtained…
We classify non-dilatonic NS-NS type II supergravity backgrounds admitting a consistent absolute parallelism. They are all given by parallelised Lie groups admitting scalar flat bi-invariant lorentzian metrics. There are seven different…
We provide explicit bounds on the difference of heights of isogenous Drinfeld modules. We derive a finiteness result in isogeny classes. In the rank 2 case, we also obtain an explicit upper bound on the size of the coefficients of modular…
A recent line of work on lattice codes for Gaussian wiretap channels introduced a new lattice invariant called secrecy gain as a code design criterion which captures the confusion that lattice coding produces at an eavesdropper. Following…
We present a geometric approach towards derandomizing the Isolation Lemma by Mulmuley, Vazirani, and Vazirani. In particular, our approach produces a quasi-polynomial family of weights, where each weight is an integer and quasi-polynomially…
We construct Euclidean lattices whose sets of minimal vectors support some large equiangular families of lines, using notably reduction modulo~$2$ of lattices. %as considered in \cite{Ma1} and \cite{Ma2}. We also consider some related…
We complete a classification of the two-vertex geometrically irreducible algebras. We also classify the algebras in new classes of hom- and ext-irreducible algebras.
The paper constructs an `exotic' algebraic 2-complex over the generalized quaternion group of order 28, with the boundary maps given by explicit matrices over the group ring. This result depends on showing that a certain ideal of the group…
Let X be a polyhedral complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When X is two-dimensional and has all links isometric to either a complete bipartite…
We show that among the Euclidean submanifolds with codimension two the ones of rank two that are parabolic but nonruled are isometrically rigid. This generalizes the result in [10] that these submanifolds are genuinely rigid. In addition,…
We consider the problem of finding lower bounds on the number of unlabeled $n$-element lattices in some lattice family. We show that if the family is closed under vertical sum, exponential lower bounds can be obtained from vertical sums of…
We give a new, purely coding-theoretic proof of Koch's criterion on the tetrad systems of Type II codes of length 24 using the theory of harmonic weight enumerators. This approach is inspired by Venkov's approach to the classification of…
In this note we settle some technical questions concerning finite rank quasi-free Hilbert modules and develop some useful machinery. In particular, we provide a method for determining when two such modules are unitarily equivalent. Along…
We show how several results about p-adic lattices generalize easily to lattices over valuation ring of arbitrary rank having only the Henselian property for quadratic polynomial. If 2 is invertible we obtain the uniqueness of the Jordan…
Let $G$ be a rank $n$ additive subgroup of $\bC$ and $\Vir[G]$ the corresponding Virasoro algebra of rank $n$. In the present paper, irreducible weight modules with finite dimensional weight spaces over $\Vir[G]$ are completely determined.…