Related papers: Forbidden lines are not quenched

A classic theorem of Euclidean geometry asserts that any noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chv\'atal conjectured that this holds for an arbitrary finite metric space, with a certain…

King's conjecture states that on every smooth complete toric variety $X$ there exists a strongly exceptional collection which generates the bounded derived category of $X$ and which consists of line bundles. We give a counterexample to this…

It is well-known to be impossible to trisect an arbitrary angle and duplicate an arbitrary cube by a ruler and a compass. On the other hand, it is known from the ancient times that these constructions can be performed when it is allowed to…

Here in particular, we give a characterization of Quasi-line Graphs in terms of forbidden induced subgraphs. In general, we prove a necessary and sufficient condition for a graph to be a union of two cliques.

We reply to Creutz's comments on our paper " 't Hooft vertices, partial quenching, and rooted staggered QCD." We show that his criticisms are incorrect and result from a misunderstanding both of our work, and of the related work of Adams.

We investigate complete non-orientable minimal surfaces of finite total curvature in $\mathbb{R}^3$ such that their ends are foliated by closed lines of curvature. This condition on the ends is necessary if they have a piece inside some…

Massive galaxies today typically are not forming stars despite being surrounded by hot gaseous halos with short central cooling times. This likely owes to some form of "quenching feedback" such as merger-driven quasar activity or radio jets…

Answering a recent question of Crochemore, we prove that the language of words that are not abelian squares is not context-free.

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.

We constructively prove that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain.

A detailed combinatorial analysis of planar convex lattice polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained.

We establish the quenched local limit theorem for reversible random walk on $\Z^d$ (with $d\ge 2$) among stationary ergodic random conductances that permit jumps of arbitrary length. The proof is based on the weak parabolic Harnack…

An elementary particle such as a photon cannot be cut in two pieces. Still it must be possible to truncate a photon with an optical shutter. The result is neither another photon nor a mix of a photon and a vacuum. Instead it is a…

Linear constraints are the linear counterpart of Haskell's class constraints. Linearly typed parameters allow the programmer to control resources such as file handles and manually managed memory as linear arguments. Indeed, a linear type…

We show that Lelek's problem on the chainability of continua with span zero is not a metric problem: from a non-metric counterexample one can construct a metric one.

Entangled inputs can enhance the capacity of quantum channels, this being one of the consequences of the celebrated result showing the non-additivity of several quantities relevant for quantum information science. In this work, we answer…

We refute the so-called one-line proof of the infinitude of primes in [1].

We prove that there is no finite-alphabet nonlocal box that generates exactly those correlations that can be generated using a maximally entangled pair of qubits. More generally, we prove that if some finite-alphabet nonlocal box is strong…

Sealing information means making it publicly available, but with the possibility of knowing if it has been read. Commenting on [1], we will show that perfect quantum sealing is not possible for perfectly retrievable information, due to the…

We prove that, with "obvious" exceptions, a CM-point (j(\tau),j(\tau')) cannot belong to a straight line in C^2 defined over Q. This generalizes a result of K\"uhne, who proved this for the line x+y=1.