Related papers: Equivalence classes of codimension one cut-and-pro…
Let $\mathcal{D}=(d_n)_{n=1}^\infty$ be a bounded sequence of integers with $d_n\ge 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i+j=1$. We prove that the set of $x \in \RR$ for which there exists some constant $c(x) >…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
This paper deals with two main topics related to Diophantine approximation. Firstly, we show that if a point on an algebraic variety is approximable by rational vectors to a sufficiently large degree, the approximating vectors must lie in…
It is proved that for any $0<\beta<\alpha$, any bounded Ahlfors $\alpha$-regular space contains a $\beta$-regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most $O(\alpha/(\alpha-\beta))$. The bound on…
A real algebraic variety W of dimension m is said to be uniformly rational if each of its points has a Zariski open neighborhood which is biregularly isomorphic to a Zariski open subset of R^m. Let l be any nonnegative integer. We prove…
We prove the existence of Local Uniformization for rational codimension one foliations along rational rank one valuations, in any ambient dimension. This result is consequence of the Truncated Local Uniformization of integrable formal…
In this paper we generalize several results on separated nets in Euclidean space to separated nets in connected simply connected nilpotent Lie groups. We show that every such group $G$ contains separated nets that are not biLipschitz…
We study nonperiodic tilings of the line obtained by a projection method with an interval projection structure. We obtain a geometric characterisation of all interval projection tilings that admit substitution rules and describe the set of…
In this paper we will see deductive systems for classical propositional and predicate logic in the calculus of structures. Like sequent systems, they have a cut rule which is admissible. In addition, they enjoy a top-down symmetry and some…
We record a particularly simple construction on top of Lumsdaine's local universes that allows for a Coquand-style universe of propositions with propositional extensionality to be interpreted in a category with subobject classifiers.
We consider the discrepancy problem of coloring $n$ intervals with $k$ colors such that at each point on the line, the maximal difference between the number of intervals of any two colors is minimal. Somewhat surprisingly, a coloring with…
Let $\pi: X \to Y$ be a morphism of projective varieties and suppose that $\alpha$ is a pseudo-effective numerical cycle class satisfying $\pi_*\alpha = 0$. A conjecture of Debarre, Jiang, and Voisin predicts that $\alpha$ is a limit of…
We consider the problem of partitioning a line segment into two subsets, so that $n$ finite measures all have the same ratio of values for the subsets. Letting $\alpha\in[0,1]$ denote the desired ratio, this generalises the PPA-complete…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
The continued fraction mapping maps a number in the interval $[0,1)$ to the sequence of its partial quotients. When restricted to the set of irrationals, which is a subspace of the Euclidean space $\mathbb{R}$, the continued fraction…
Based on the intuitive notion of convexity, we formulate a universal property defining interval objects in a category with finite products. Interval objects are structures corresponding to closed intervals of the real line, but their…
We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice expansions. This result encompasses Ghilardi-Meloni's and Suzuki's…
By using nonstandard analysis, we prove embeddability properties of difference sets $A-B$ of sets of integers. (A set $A$ is "embeddable" into $B$ if every finite configuration of $A$ has shifted copies in $B$.) As corollaries of our main…
The Constraint Satisfaction Problem (CSP) has been intensively studied in many areas of computer science and mathematics. The approach to the CSP based on tools from universal algebra turned out to be the most successful one to study the…
The purpose of this article is to give an interpretation of real projective structures and associated cohomology classes in terms of connections, sections, etc. satisfying elliptic partial differential equations in the spirit of Hodge…