相关论文: Plinths and Pedestals
This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the…
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a formal definition for the concept of center in both cases.…
Over the past twenty years, lecture hall partitions have emerged as fundamental combinatorial structures, leading to new generalizations and interpretations of classical theorems and new results. In recent years, geometric approaches to…
We count tilings of the $n \times m$ rectangular grid, cylinder, and torus with arbitrary tile sets up to arbitrary symmetries of the square and rectangle, along with cyclic shifting of rows and columns. This provides a unifying framework…
This paper is a continuation of an earlier one, and completes a classification of the configurations of points in a plane lattice that determine angles that are rational multiples of ${\pi}$. We give a complete and explicit description of…
In this note we compute some enumerative invariants of real and complex projective spaces by means of some enriched graphs called floor diagrams.
Mass partition problems describe the partitions we can induce on a family of measures or finite sets of points in Euclidean spaces by dividing the ambient space into pieces. In this survey we describe recent progress in the area in addition…
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane.
A survey of tilings in the plane for a general audience.
In this study, the properties of an oscillating system composed of a pendulum connected to a seesaw and placed on a moving platform with a certain slope are analyzed. Using complex numbers to collect the information contained in the system…
This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.
An intriguing correspondence between certain finite planar tessellations and the Descartes circle arrangements is presented. This correspondence may be viewed as a visualization of the spinor structure underlying Descartes circles.
A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and…
Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…
We discuss the practical problems arising when constructing any (new or old) scales on slide rules, i.e. realizing the theory in the practice. This might help anyone in planning and realizing (mainly the magnitude and labeling of) new…
Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…
We present algebraic and geometric arguments that give a complete classification of the rational normal scrolls that are hyperplane section of a given rational normal scrolls.
The statistics of meander and related problems are studied as particular realizations of compact polymer chain foldings. This paper presents a general discussion of these topics, with a particular emphasis on three points: (i) the use of a…
A planar integral point set is a set of non-collinear points in plane such that for any pair of the points the Euclidean distance between the points is integral. We discuss the classification of planar integral point sets and provide…
For stacked simplicial complexes, (special subclasses of such are: trees, triangulations of polygons, stacked polytopes), we give an explicit bijection between partitions of facets (for trees: edges), and partitions of vertices into…