相关论文: Bordered magic squares: elements for a comprehensi…
At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific…
The recently introduced polynomial time integration framework proposes a novel way to construct time integrators for solving systems of first-order ordinary differential equation by using interpolating polynomials in the complex time plane.…
We introduce Magic Gems, a geometric representation of magic squares as three-dimensional polyhedra. By mapping an n times n magic square onto a centered coordinate grid with cell values as vertical displacements, we construct a point cloud…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
This work concerns with the following problem. Given a two-dimensional domain whose boundary is a closed polygonal line with internal boundaries defined also by polygonal lines, it is required to generate a grid consisting only of…
Historically, games of all kinds have often been the subject of study in scientific works of Computer Science, including the field of machine learning. By using machine learning techniques and applying them to a game with defined rules or a…
The General AI Challenge is an initiative to encourage the wider artificial intelligence community to focus on important problems in building intelligent machines with more general scope than is currently possible. The challenge comprises…
We present, to the best of the authors' knowledge, all known results for the (planar) crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
New algorithms for generating closed knight's tours are obtained by generating a vertex-disjoint cycle cover of the knight's graph and joining the resulting cycles. It is shown experimentally that these algorithms are significantly faster…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…
In this articles we consider very mathematical (if not very plausible) geometric marching. Our marchers will exhibit beautiful mathematics, some familiar and some less so. In a final summary section we discuss the point of all the fancy…
In this survey we describe a recently-developed technique for bounding the number (and controlling the typical structure) of finite objects with forbidden substructures. This technique exploits a subtle clustering phenomenon exhibited by…
Here, we propose a clustering technique for general clustering problems including those that have non-convex clusters. For a given desired number of clusters $K$, we use three stages to find a clustering. The first stage uses a hybrid…
The article addresses balanced clustering problems with an additional requirement as a tree-like structure over the obtained balanced clusters. This kind of clustering problems can be useful in some applications (e.g., network design,…
We propose a notion of a generalized order, which can be used for the notion of a strict partial order. We introduce a weak order to replace the usual weak order defined from a strict partial order. In a constructive setting, that usual…
We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical \v{S}arkovski\u{i}…
Based on the rules of magic cubes, a game of two-dimensional magic cube was deliberately designed. This essay will explore its properties with the assistance of group theory and computer programming. It will first elaborate the rules of…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.