Related papers: A note on lattice coverings
We give here the specific product rule for the lattice of questions. This product rule differs from the product rule for the lattice of statements, hence the qualifier `specific'. This is because the elements in the lattice of statements…
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
Functions that satisfy the Hadamard Fisher Inequalities also satisfy Newton's Inequalities
I give a brief introduction to lattice QCD for non-specialists.
These are the notes from my courses on the arithmetic of quadratic forms.
Recently Mertens and Moore [arXiv:1909.01484v1] showed that site percolation "is odd." By this they mean that on an $M\times N$ square lattice the number of distinct site configurations that allow for vertical percolation is odd. We report…
In the present study we consider an example of a boundary value problem for a simple second order ordinary differential equation, which may exhibit a boundary layer phenomenon. We show that usual central finite differences, which are second…
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tiles that lattice by translations, in fact tiles periodically. We announce here a disproof of this conjecture for sufficiently large $d$, which…
At a first glance, the problem of illuminating the boundary of a convex body by external light sources and the problem of covering a convex body by its smaller positive homothetic copies appear to be quite different. They are in fact two…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
In the absence of decoherence the current of fermionic particles across a finite lattice connecting two reservoirs (leads) with different chemical potentials is known to be ballistic. It is also known that decoherence typically suppresses…
Lattices induced by coverings arise naturally in matroid theory and combinatorial optimization, providing a structured framework for analyzing relationships between independent sets and closures. In this paper, we explore the structural…
A recursive scheme relying on decagons is used to generate Penrose-like sublattices or tilings. Its relevance for understanding structures with non-crystallographic symmetry is discussed.
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
Covering numbers of convex bodies based on homothetical copies and related illumination numbers are well-known in combinatorial geometry and, for example, related to Hadwiger's famous covering problem. Similar numbers can be defined by…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
Most comparisons of preferences are instances of single-crossing dominance. We examine the lattice structure of single-crossing dominance, proving characterisation, existence and uniqueness results for minimum upper bounds of arbitrary sets…
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
In this note we show that ribbon concordance forms a partial ordering on the set of knots, answering a question of Gordon. The proof makes use of representation varieties of the knot groups to $SO(N)$ and relations between them induced by a…
An updated review is presented of lattice investigations of colour confinement.