Related papers: Patterns formed by coins
We analyze the main arguments that attempt to explain why there is no point in changing the envelope. Most people confuse estimation and calculation, conditional and unconditional probabilities, random and non-random variables, modelling…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
In this paper we investigate the problem of sorting a set of $n$ coins, each with distinct but unknown weights, using an unusual scale. The classical version of this problem, which has been well-studied, gives the user a binary scale,…
Approximate but reliable solutions of a quantum system with $N$ identical particles can be easily computed with the envelope theory, also known as the auxiliary field method. This technique has been developed for Hamiltonians with arbitrary…
The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct…
The simple connected graphs may be classified by their cycle composition (number and lengths of cycles). This work derives the counting series of the simple connected graphs that have cycles of unrestricted number and length, but no…
We compute the number of equivalence classes of nonperiodic covering cycles of given length in a non oriented connected graph. A covering cycle is a closed path that traverses each edge of the graph at least once. A special case is the…
A new ordering, extending the notion of universal cycles of Chung {\em et al.} (1992), is proposed for the blocks of $k$-uniform set systems. Existence of minimum coverings of pairs by triples that possess such an ordering is established…
In this article we generalize packing density problems from permutations to patterns with repeated letters and generalized patterns. We are able to find the packing density for some classes of patterns and several other short patterns.
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…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
From the geometric study of the elementary cell of hexagonal circle packings --- a flower of 7 circles --- the class of conformally symmetric circle packings is defined. Up to Moebius transformations, this class is a three parameter family,…
Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…
This article provides a convenient framework for quantitative evaluation of the entanglement generated when two structureless, distinguishable particles scatter non-relativistically in one dimension. It explores how three factors determine…
The Schmidt arrangement of an imaginary quadratic number field $K$ is the orbit of the extended real line under $\text{PSL}(2, \mathcal{O}_K)$ as M\"obius transformations on the extended complex plane. If $K\neq\mathbb{Q}(\sqrt{-3})$, then…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We determine the distribution of nearest neighbour spacings between the tangencies to a fixed circle in a class of circle packings generated by reflections. We use a combination of geometric tools and the theory of automorphic forms.
We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles,…