相关论文: On the generalization of the Costas property to hi…
A novel higher-dimensional definition for Costas arrays is introduced. This definition works for arbitrary dimensions and avoids some limitations of previous definitions. Some non-existence results are presented for multidimensional Costas…
A Costas array is a permutation array for which the vectors joining pairs of $1$s are all distinct. We propose a new three-dimensional combinatorial object related to Costas arrays: an order $n$ Costas cube is an array $(d_{i,j,k})$ of size…
We extend the definition of the Costas property to functions in the continuum, namely on intervals of the reals or the rationals, and argue that such functions can be used in the same applications as discrete Costas arrays. We construct…
For a permutation $\pi$, and the corresponding permutation matrix, we introduce the notion of {\em discrete derivative}, obtained by taking differences of successive entries in $\pi$. We characterize the possible derivatives of…
There is a rich history of domino tilings in two dimensions. Through a variety of techniques we can answer questions such as: how many tilings are there of a given region or what does the space of all tilings look like? These questions and…
A Costas array of order $n$ is an arrangement of dots and blanks into $n$ rows and $n$ columns, with exactly one dot in each row and each column, the arrangement satisfying certain specified conditions. A dot occurring in such an array is…
A collection of open problems in Costas arrays is presented, classified into several categories, along with the context in which they arise.
A Costas latin square of order n is a set of n disjoint Costas arrays of the same order. Costas latin squares are studied here from a construction as well as a classification point of view. A complete classification is carried out up to…
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
We generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact…
Complex structures can only form in a universe that allows for bound states. While this is clearly observed in three-dimensions, added degrees of freedom in a higher-dimensional space preclude the immediate assumption that binding…
We extend the classical definition of {\it width} to higher dimensional, smooth codimension 2 knots and show in each dimension there are knots of arbitrarily large width.
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Lorentz covariant generalisations of the notions of supersymmetry, superspace and self-duality are discussed. The essential idea is to extend standard constructions by allowing tangent vectors and coordinates which transform according to…
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have more than one type change loci. In an example-driven…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…
In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
In this second of three introductory papers, we extend the notion of generalised Cesaro summation/convergence to the more natural setting of what we call remainder Cesaro summation/convergence. This greatly expands the range of problems…