Related papers: Sequences with thirteen-valued cross correlations

We investigate the effect of sequentiallydisrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two…

Let $S_{\rm div}(n)$ denote the set of permutations $\pi$ of $n$ such that for each $1\leq j \leq n$ either $j \mid \pi(j)$ or $\pi(j) \mid j$. These permutations can also be viewed as vertex-disjoint directed cycle covers of the divisor…

We study the time dependent cross correlations of stock returns, i.e. we measure the correlation as the function of the time shift between pairs of stock return time series using tick-by-tick data. We find a weak but significant effect…

In a previous it was shown that the Dedkind sums $12s(m,n)$ and $12s(x,n)$, $1\le m,x\le n$, $(m,n)=(x,n)=1$, are equal mod $\Z$ if, and only if, $(x-m)(xm-1)\equiv 0$ mod $n$. Here we determine the cardinality of numbers $x$ in the above…

Traditionally, knot theorists have considered projections of knots where there are two strands meeting at every crossing. A triple crossing is a crossing where three strands meet at a single point, such that each strand bisects the…

The sequence a_1,...,a_m is a common subsequence in the set of permutations S = {p_1,...,p_k} on [n] if it is a subsequence of p_i(1),...,p_i(n) and p_j(1),...,p_j(n) for some distinct p_i, p_j in S. Recently, Beame and Huynh-Ngoc (2008)…

We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long…

A generic uniformly distributed random sequence on the unit interval has Poissonian pair correlations. At the same time, there are only very few explicitly known examples of sequences with this property. Moreover, many types of…

We present a linear programming based algorithm for computing a spanning tree $T$ of a set $P$ of $n$ points in $\Re^d$, such that its crossing number is $O(\min(t \log n, n^{1-1/d}))$, where $t$ the minimum crossing number of any spanning…

We say that a sequence $\{x_n\}_{n \geq 1}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*} \lim_{N \rightarrow \infty} \frac{1}{N} \# \left\{ 1 \leq l \neq m \leq N \, : \, \left\lVert x_l-x_m \right\rVert < \frac{s}{N}…

A general explicit upper bound is obtained for the proportion $P(n,m)$ of elements of order dividing $m$, where $n-1 \le m \le cn$ for some constant $c$, in the finite symmetric group $S_n$. This is used to find lower bounds for the…

Chains with long-range interactions are considered. The interactions are defined such that each nth particle interacts only with chain particles with the numbers n+a(m) and n-a(m), where m=1,2,3,... and a(m) is an integer-valued function.…

For random percolation at p_c, the probability distribution P(n) of the number of spanning clusters (n) has been studied in large scale simulations. The results are compatible with $P(n) \sim \exp(-an^2)$ for all dimensions. We also study…

In the paper, we introduce a new measure of correlation between possibly non-stationary series. As the measure is based on the detrending moving-average cross-correlation analysis (DMCA), we label it as the DMCA coefficient…

In this paper, we study the distribution of consecutive patterns in the set of 123-avoiding permutations and the set of 132-avoiding permutations, that is, in $\mathcal{S}_n(123)$ and $\mathcal{S}_n(132)$. We first study the distribution of…

Let $q$ be a positive integer and $\mathcal{S}=\left\{x_0,x_1,\ldots,x_{T-1}\right\}\subseteq\mathbb{Z}_q=\{0,1,\ldots,q-1\}$ with $$0\leq x_0<x_1<\ldots< x_{T-1}\leq q-1.$$ We derive from $\mathcal{S}$ three (finite) sequences. 1. For an…

We calculate the triple correlations for the truncated divisor sum $\lambda_{R}(n)$. The $\lambda_{R}(n)$'s behave over certain averages just as the prime counting von Mangoldt function $\Lambda(n)$ does or is conjectured to do. We also…

In this paper, we explore some interesting applications of the matrix tree theorem. In particular, we present a combinatorial interpretation of a distribution of $(n-1)^{n-1}$, in the context of uprooted spanning trees of the complete graph…

The theoretical description of the correlations between observables in two separated rapidity intervals for AA-interactions at high energies is presented. In the case with the realistic nucleon distribution density of colliding nuclei the…

This work sheds some light on the relationship between a distribution's standard deviation and its range, a topic that has been discussed extensively in the literature. While many previous studies have proposed inequalities or relationships…