Related papers: Maximal integral simplices with no interior intege…
A topological space $X$ is called resolvable if it contains a dense subset with dense complement. Using only basic principles, we show that whenever the space $X$ has a resolving subset that can be written as an at most countably infinite…
In this paper we prove in certain n-dimensional normed spaces X the existence of full-dimensional equilateral simplices of large size inscribed to the unit ball B. This extends the construction of Makeev [Mak] in dimension 4 and we also…
Let X be the moduli space of SL(3,C) representations of a free group of rank r. In this paper we describe maximal algebraically independent subsets of certain minimal sets of coordinate functions on X. These subsets locally parametrize the…
We prove that the discrete Hardy-Littlewood maximal function associated with Euclidean spheres with small radii has dimension-free estimates on $\ell^p(\mathbb{Z}^d)$ for $p\in[2,\infty).$ This implies an analogous result for the Euclidean…
The notion of {\it free} generalized vertex algebras is introduced. It is equivalent to the notion of {\it generalized principal subspaces} associated with lattices which are not necessarily integral. Combinatorial bases and the characters…
An n-dimensional simplex \Delta in \R^n is called empty lattice simplex if \Delta \cap\Z^n is exactly the set of vertices of \Delta . A theorem of G. K. White shows that if n=3 then any empty lattice simplex \Delta \subset\R^3 is isomorphic…
We present integrable lattice equations on a two dimensional square lattice with coupled vertex and bond variables. In some of the models the vertex dynamics is independent of the evolution of the bond variables, and one can write the…
We show that every cubic bridgeless graph with n vertices has at least 3n/4-10 perfect matchings. This is the first bound that differs by more than a constant from the maximal dimension of the perfect matching polytope.
Affine manifolds are called integral if there is an atlas such that all transition maps are affine transformations with integer matrices of linear parts. In this paper we describe all complete integral affine structures on compact…
We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3) TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold…
A set of integers is sum-free if it contains no solution to the equation $x+y=z$. We study sum-free subsets of the set of integers $[n]=\{1,\ldots,n\}$ for which the integer $2n+1$ cannot be represented as a sum of their elements. We prove…
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the alge- braic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras…
We prove an explicit asymptotic formula for the logarithm of the minimal ranks of $n$-universal lattices over the ring of integers of totally real number fields. We also show that, for any constant $C > 0$ and $n \geq 3$, there are only…
Recently $C^m$-conforming finite elements on simplexes in arbitrary dimension are constructed by Hu, Lin and Wu. The key in the construction is a non-overlapping decomposition of the simplicial lattice in which each component will be used…
We study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to this order. We show that the only locally finite graphs which…
We show that a complete embedded maximal surface in the 3-dimensional Lorentz-Minkowski space $L^3$ with a finite number of singularities is, up to a Lorentzian isometry, an entire graph over any spacelike plane asymptotic to a vertical…
For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…
It is known that there are finitely many simplicial complexes (up to isomorphism) with a given number of vertices. Translating to the language of $h$-vectors, there are finitely many simplicial complexes of bounded dimension with $h_1=k$…
Let $\Gamma$ be a group which is virtually free of rank at least 2 and let $\mathcal{F}_{td}(\Gamma)$ be the family of totally disconnected, locally compact groups containing $\Gamma$ as a co-compact lattice. We prove that the values of the…
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…