相关论文: The Integer Decomposition Property and Weighted Pr…
We study fully convex polygons with a given area, and variable perimeter length on square and hexagonal lattices. We attach a weight t^m to a convex polygon of perimeter m and show that the sum of weights of all polygons with a fixed area s…
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Given a shifted order ideal $U$, we associate to it a family of simplicial complexes $(\Delta_t(U))_{t\geq 0}$ that we call squeezed complexes. In a special case, our construction gives squeezed balls that were defined and used by Kalai to…
It is shown that a (curved) projective structure on a smooth manifold determines on the Poisson algebra of smooth, fiberwise-polynomial functions on the cotangent bundle a one-parameter family of graded star products. For a particular value…
First, we calculate the Ehrhart polynomial associated to an arbitrary cube with integer coordinates for its vertices. Then, we use this result to derive relationships between the Ehrhart polynomials for regular lattice tetrahedrons and…
We present a new type of basis set which is local, compact, and orthogonal. The basis functions, called orthlets, are centered at the sites of a lattice and are specifically adapted to represent the system being studied. The adaptability…
We describe weighted projective lines in the sense of Geigle and Lenzing by a moduli problem on the canonical algebra of Ringel. We then go on to study generators of the derived categories of coherent sheaves on the total spaces of their…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
Fix an odd prime $p$ and let $X$ be the $p$-localization of a finite suspended $CW$-complex. Given certain conditions on the reduced mod-$p$ homology $\bar H_*(X;\zmodp)$ of $X$, we use a decomposition of $\Omega\Sigma X$ due to the second…
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\mathbb{Z}^2$. We first prove a formula on the rotation number of a…
We define the concept of weighted lattice polynomial functions as lattice polynomial functions constructed from both variables and parameters. We provide equivalent forms of these functions in an arbitrary bounded distributive lattice. We…
We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets…
We prove that the problem of minimizing the number of integer points inparallel translations of a rational convex polytope in $\mathbb{R}^6$ is NP-hard. We apply this result to show that given a rational convex polytope $P \subset…
The reconstruction problem of voxels with individual weightings can be modeled a position- and angle- dependent function in the forward-projection. This changes the system matrix and prohibits to use standard filtered backprojection. In…
Recently $C^m$-conforming finite elements on simplexes in arbitrary dimension are constructed by Hu, Lin and Wu. The key in the construction is a non-overlapping decomposition of the simplicial lattice in which each component will be used…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
We study how geometric properties of tropical convex sets and polytopes, which are of interest in many application areas, manifest themselves in their algebraic structure as modules over the tropical semiring. Our main results establish a…
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletion-contraction properties do not hold. We construct a polynomial for polymatroids which behaves similarly to the Tutte polynomial of a…
The Fine interior $F(P)$ of a $d$-dimensional lattice polytope $P \subset {\Bbb R}^d$ is the set of all points $y \in P$ having integral distance at least $1$ to any integral supporting hyperplane of $P$. We call a lattice polytope…
We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…