Related papers: A note on lattice coverings
We give short and simple proofs of what seem to be folklore results: * the maximum cardinality of the intersection of a lattice cube with an affine subspace; * the minimum number of affine subspaces needed to cover a lattice cube.
This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the "tiles" have elastic size, and that the order of placement is significant. Spotlight…
The purpose of this note is to give a self contained description of Walls finiteness obstruction.
We describe the construction of the slice fibration of a given one.
The point of this short note concerns with two facts on the scheme of secant loci. The first one is an attempt to describe the tangent cone of these schemes globally and the second one is a comparision on the dimension of the tangent spaces…
I discuss some of the historical circumstances that drove us to use the lattice as a non-perturbative regulator. This approach has had immense success, convincingly demonstrating quark confinement and obtaining crucial properties of the…
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able…
We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…
New cases of the multiplicity conjecture are considered.
A lattice $\Lambda$ is said to be an extension of a sublattice $L$ of smaller rank if $L$ is equal to the intersection of $\Lambda$ with the subspace spanned by $L$. The goal of this paper is to initiate a systematic study of the geometry…
A general theorem on fibers of singular sets is presented.
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
In this note we provide a simple formula of general term of recurrent sequence.
The structure of a previously developed representation of the Leech lattice, $\Lambda_{24}$, is exposed to further light with this unified and very simple construction.
In this note we prove a weighted version of the Khintchine inequalities.
Cutting out and object and estimate its transparency mask is a key task in many applications. We take on the work on closed-form matting by Levin et al., that is used at the core of many matting techniques, and propose an alternative…
The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem approximately, rather than exactly, and in the proof of a…
In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.