相关论文: Bordered magic squares: elements for a comprehensi…
The study of knot mosaics is based upon representing knot diagrams using a set of tiles on a square grid. This branch of knot theory has many unanswered questions, especially regarding the efficiency with which we draw knots as mosaics.…
A knot mosaic is a representation of a knot or link on a square grid using a collection of tiles that are either blank or contain a portion of the knot diagram. Traditionally, a piece of the knot on one tile connects to a piece of the knot…
Quantum phenomena have remained largely inaccessible to the general public. This can be attributed to the fact that we do not experience quantum mechanics on a tangible level in our daily lives. Games can provide an environment in which…
In this paper we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique…
A defining feature of collectable card games is the deck building process prior to actual gameplay, in which players form their decks according to some restrictions. Learning to build decks is difficult for players and models alike due to…
A generic rectangulation is a partition of a rectangle into finitely many interior-disjoint rectangles, such that no four rectangles meet in a point. In this work we present a versatile algorithmic framework for exhaustively generating a…
When defining the amount of additive structure on a set it is often convenient to consider certain sumsets; Calculating the cardinality of these sumsets can elucidate the set's underlying structure. We begin by investigating finite sets of…
We provide a spectrum of results for the Universal Guard Problem, in which one is to obtain a small set of points ("guards") that are "universal" in their ability to guard any of a set of possible polygonal domains in the plane. We give…
We study biased Maker-Breaker games on a graph system $\{G_1,\ldots,G_s\}$, in which Maker's goal is to claim certain rainbow structures, i.e., specified subgraphs consisting of at most one edge from each graph $G_i$. We consider the…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
We review a general parameterization of an order-3 magic square derived by Lucas and we compound it to produce a parameterized order-9 magic square. Sequential compounding to higher order also is treated. Expressions are found for the…
This paper describes a novel method of generating hex-dominant meshes using pre-computed optimal subdivisions of the unit cube in a grid-based approach. Our method addresses geometries that are standard in mechanical engineering and often…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
We settle the existence of certain "anti-magic" cubes using combinatorial block designs and graph decompositions to align a handful of small examples.
This paper develops a clustering method that takes advantage of the sturdiness of model-based clustering, while attempting to mitigate some of its pitfalls. First, we note that standard model-based clustering likely leads to the same number…
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
Boundary element methods (BEM) reduce a partial differential equation in a domain to an integral equation on the domain's boundary. They are particularly attractive for solving problems on unbounded domains, but handling the dense matrices…
A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…
The game of nim, with its simple rules, its elegant solution and its historical importance is the quintessence of a combinatorial game, which is why it led to so many generalizations and modifications. We present a modification with a new…