Related papers: A product chain without cutoff

We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…

Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic…

It was recently proved that every planar graph is a subgraph of the strong product of a path and a graph with bounded treewidth. This paper surveys generalisations of this result for graphs on surfaces, minor-closed classes, various…

We study the time that the simple exclusion process on the complete graph needs to reach equilibrium in terms of total variation distance. For the graph with n vertices and 1<<k<n/2 particles we show that the mixing time is of order…

For every $n$, we construct two curves in the plane that intersect at least $n$ times and do not form spirals. The construction is in three stages: we first exhibit closed curves on the torus that do not form double spirals, then arcs on…

Dujmovi\'c et al. [\emph{J.~ACM}~'20] recently proved that every planar graph is isomorphic to a subgraph of the strong product of a bounded treewidth graph and a path. Analogous results were obtained for graphs of bounded Euler genus or…

We show there is no categorical metric continuum. This means that for every metric continuum X there is another metric continuum Y such that X and Y have (countable) elementarily equivalent bases but X and Y are not homeomorphic. As an…

This article presents the further steps of the previously done studies taking into consideration the k-th order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex…

Let $k$ be an algebraically closed field of characteristic $p > 0$. Let $X$ be an irreducible smooth projective curve of genus $g$ over $k$. Fix an integer $n \geq 2$, and let $S^n(X)$ be the $n$-fold symmetric product of $X$. In this…

We introduce the abstract notion of a chain, which is a sequence of $n$ points in the plane, ordered by $x$-coordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general…

We present examples of closed subsets of a free group such that their product is not closed in the profinite topology. We discuss how to characterize a subset of a free group which is closed in the profinite topology and its product with…

Let T be a complete discrete valuation ring and $\hat{X}$ a smooth projective curve over $S=\spec(T)$ with closed fibre $X$. Denote by $F$ the function field of $\hat{X}$ and by $\hat{F}$ the completion of $F$ with respect to the discrete…

The geometry of divisors on algebraic curves has been studied extensively over the years. The foundational results of this Brill-Noether theory imply that on a general curve, the spaces parametrizing linear series (of fixed degree and…

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…

Families of symmetric simple random walks on Cayley graphs of Abelian groups with a bound on the number of generators are shown to never have sharp cut off in the sense of [1], [3], or [5]. Here convergence to the stationary distribution is…

We study linkedness of Cartesian product of graphs and prove that the product of an $a$-linked and a $b$-linked graphs is $(a+b-1)$-linked if the graphs are sufficiently large. Further bounds in terms of connectivity are shown. We determine…

A feed-forward neural network is demonstrated to efficiently unfold the energy distribution of protons and alpha particles passing through passive material. This model-independent approach works with unbinned data and does not require…

Coherence in a monoidal category asserts that all morphisms built from structural isomorphisms with a fixed source and target coincide. These structural isomorphisms include, in particular, the associators. Linearly distributive categories…

We first give a sufficient condition for a Mal'cev-Neumann ring of formal series to be a noncrossed product division algebra. This result is then used to give an elementary proof of the existence of noncrossed product division algebras (of…

The sequence of middle divisors is shown to be unbounded. For a given number $n$, $a_{n,0}$ is the number of divisors of $n$ in between $\sqrt{n/2}$ and $\sqrt{2n}$. We explicitly construct a sequence of numbers $n(i)$ and a list of…