Related papers: On the Correlation Distribution for a Ternary Niho…
We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees, with interesting consequences for enumeration, mesh compression and graph sampling. Our bijection yields an efficient uniform random…
Ordinary binary multiplication of natural numbers can be generalized in a non-trivial way to a ternary operation by considering discrete volumes of lattice hexagons. With this operation, a natural notion of `3-primality' -- primality with…
A well known result in the theory of uniform distribution modulo one (which goes back to Fej\'er and Csillag) states that the fractional parts $\{n^\alpha\}$ of the sequence $(n^\alpha)_{n\ge1}$ are uniformly distributed in the unit…
In this paper we extend the works \cite{gegeng2,XLZD} further in two directions and compute the weight distribution of these cyclic codes under more relaxed conditions. It is interesting to note that many cyclic codes in the family are…
We study the convergence of distributions on finite paths of weighted digraphs, namely the family of Boltzmann distributions and the sequence of uniform distributions. Targeting applications to the convergence of distributions on paths, we…
The static pair correlation (distribution) function and the structure factor of particle distributions in three-dimensional homogeneous isotropic systems are explicitly restored from two-dimensional data observed in a thin slab sliced out…
For an odd prime $p$ and two positive integers $n\geq 3$ and $k$ with $\frac{n}{{\rm gcd}(n,k)}$ being odd, the paper determines the weight distribution of a $p$-ary cyclic code $\mathcal{C}$ over $\mathbb{F}_{p}$ with nonzeros…
We consider an array of random variables, taking values in a complete and separable metric space, that exhibits a kind of symmetry which we call row exchangeability. Given such an array, a natural model for Bayesian nonparametric inference…
The standard proof of NP-Hardness of 3DM provides a power-$4$ reduction of 3SAT to 3DM. In this note, we provide a linear-time reduction. Under the exponential time hypothesis, this reduction improves the runtime lower bound from…
Six semi-detached Algol-type binaries lacking a period analysis were chosen to test for a presence of a third body. The O-C diagrams of these binaries were analyzed with the least-squares method by using all available times of minima. Also…
We present the first next-to-next-to-next-to-leading order (N$^3$LO) calculation of the twist-2 matching coefficients for transverse momentum dependent (TMD) quark transversity parton distribution and fragmentation functions in QCD. This…
We present measurements of the spatial clustering statistics in redshift space of various scalar field modified gravity simulations. We utilise the two-point and the three-point correlation functions to quantify the spatial distribution of…
Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem in 1973 concerning the pair correlation of zeros of the Riemann zeta-function and applied this to prove that at least $2/3$ of the zeros are simple. In this paper, we…
The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation…
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher dimensions. Roughly speaking, in the one-dimensional setting,…
For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…
A theory of systems with long-range correlations based on the consideration of binary N-step Markov chains is developed. In our model, the conditional probability that the i-th symbol in the chain equals zero (or unity) is a linear function…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. Let $m=2\ell+1$ for an integer $\ell\geq 1$…
Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function $\zeta$ of galaxies, to the third order density perturbations. We make the…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem…