Related papers: The densest sequence in the unit circle

Given any $\varepsilon>0$ we prove that every sufficiently large $n$-vertex $3$-graph $H$ where every pair of vertices is contained in at least $(1/3+\varepsilon)n$ edges contains a copy of $C_{10}$, i.e.\ the tight cycle on $10$ vertices.…

We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This…

We show that the closure of the value set of a real linear recurrence sequence is the union of a countable set and a finite collection of intervals. Conversely, any finite collection of closed intervals is the closure of the value set of…

We introduce a notion of density which extends both the notion of Lelong number and the theory of intersection for positive closed currents on Kaehler manifolds. For arbitrary finite family of positive closed currents on a compact Kaehler…

Let $L$ be a finite-dimensional real normed space, and let $B$ be the unit ball in $L$. The sign sequence constant of $L$ is the least $t>0$ such that, for each sequence $v_1, \ldots, v_n \in B$, there are signs $\varepsilon_1, \ldots,…

Let U(N) denote the maximal length of arithmetic progressions in a random uniform subset of {0,1}^N. By an application of the Chen-Stein method, we show that U(N)- 2 log(N)/log(2) converges in law to an extreme type (asymmetric)…

In most direct estimates of the mass density (visible or dark) of the Universe, a central input parameter is the luminosity density of the Universe. Here we consider the measurement of this luminosity density from red-shift surveys, as a…

This paper is part of the ongoing effort to study high-dimensional permutations. We prove the analogue to the Erd\H{o}s-Szekeres theorem: For every $k\ge1$, every order-$n$ $k$-dimensional permutation contains a monotone subsequence of…

We report the discovery of a probable large scale structure composed of many galaxy clumps around the known twin clusters at z=1.26 and z=1.27 in the Lynx region. Our analysis is based on deep, panoramic, and multi-colour imaging…

We present new Chandra observations of a high redshift (z~1) galaxy cluster discovered in the Red-Sequence Cluster Survey (RCS): RCS043938-2904.7. X-ray luminosity measurements and mass estimates are consistent with L_X-T_X and M_delta-T_X…

The clustering of nucleons in nuclei is a widespread but elusive phenomenon for study. Here, we wish to highlight the variety of theoretical approaches, and demonstrate how they are mutually supportive and complementary. On the experimental…

We define the cyclic matching sequencibility of a graph to be the largest integer $d$ such that there exists a cyclic ordering of its edges so that every $d$ consecutive edges in the cyclic ordering form a matching. We show that the cyclic…

The intrinsic volumes are measures of the content of a convex body. This paper uses probabilistic and information-theoretic methods to study the sequence of intrinsic volumes of a convex body. The main result states that the intrinsic…

This paper focuses on the asymptotic behaviors of the length of the largest 1-cluster in a finite iid Bernoulli sequence. We first reveal a critical phenomenon on the length and then study its limit distribution.

It is known that the $S(n,k)$ Stirling numbers as well as the ordered Stirling numbers $k!S(n,k)$ form log-concave sequences. Although in the first case there are many estimations about the mode, for the ordered Stirling numbers such…

Let $\theta $ be a Salem number and $P(x)$ a polynomial with integer coefficients. It is well-known that the sequence $(\theta^n)$ modulo 1 is dense but not uniformly distributed. In this article we discuss the sequence $(P(\theta^n))$…

We present the results of Chandra observations of 13 optically-selected clusters with 0.6<z< 1.1, discovered via the Red-sequence Cluster Survey (RCS). All but one are detected at S/N>3; though 3 were not observed long enough to support…

We prove the density of the sets of the form ${{\lambda}_1^m {\mu}_1^n {\xi}_1 +...+{\lambda}_k^m {\mu}_k^n {\xi}_k : m,n \in \mathbb N}$ modulo one, where $\lambda_i$ and $\mu_i$ are multiplicatively independent algebraic numbers…

We propose a phenomenological equation for the vortex line density in rotating Bose-Einstein condensates as a function of the angular speed. This equation provides a simple description of the gross features of the increase in vortex number…

Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…