Related papers: Note on half-cube embeddings

In this note, we show that a part of [5, Remark 2.2] is not correct. Some conditions are given under which the same holds.

We prove that the combinatorial optimization problem of determining the hull number of a partial cube is NP-complete. This makes partial cubes the minimal graph class for which NP-completeness of this problem is known and improves some…

Some basic geometric properties of doubly twisted product immersions are established.

Due to the recent renewal in the interest for embedded surfaces we provide a list of commented references of interest.

We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…

We study $n$-dimensional matrices with $\{0,1\}$-entries ($n$-cubes) such that all their $2$-dimensional slices are incidence matrices of symmetric designs. A known construction of these objects obtained from difference sets is generalized…

This is a follow up on our previous work in which we have presented a modified, simpler version of the remarkable recent result of Christodoulou on the formation of trapped surfaces. In this paper we prove two related results. First we…

We give a generalization of Meeks-Yau's celebrated embeddedness result for the solutions of the Plateau problem for extreme curves.

The exposition has been significantly altered, hopefully improved.

We present a list of possible effective theories which may describe a QHE edge at filling fraction $\nu =5/2$. We show that there exist several abelian and non-abelian effective theories (apart from those discussed in the literature)…

We prove a semi-global result on the existence of conformal embeddings of the two-sphere into the round three-sphere S^3(1) with prescribed mean curvature.

Quantum annealing promises to be an effective heuristic for complex NP-hard problems. However, clear demonstrations of quantum advantage are wanting, primarily constrained by the difficulty of embedding the problem into the quantum…

The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.

The study of embeddings of smooth manifolds into Euclidean and projective spaces has been for a long time an important area in topology. In this paper we obtain improvements of classical results on embeddings of smooth manifolds, focusing…

In [15] the authors proved the Pugh-Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e. stable ergodic diffeomorphism are dense among the partially hyperbolic ones. In this work we address the issue of…

We study the existence of cubic quotients of finite-dimensional quasi-normed spaces, that is, quotients well isomorphic to $\ell_{\infty}^k$ for some $k.$ We give two results of this nature. The first guarantees a proportional dimensional…

We prove a general embedding theorem for Cohen--Macaulay curves (possibly nonreduced), and deduce a cheap proof of the standard results on pluricanonical embeddings of surfaces, assuming vanishing H^1(2K_X)=0.

Given a finite volume hyperbolic surface, a fundamental polygon and an oriented closed geodesic, we associate a partial covering of the surface. We prove that given a sequence of collections of oriented closed geodesics equidistributing in…

We establish a $p$-adic analogue of a recent significant result of Ren-Wang (arXiv:2308.08819) on Furstenberg sets in the Euclidean plane. Building on the $p$-adic version of the high-low method from Chu (arXiv:2510.20104), we analyze…

We prove two conjectures on weighted complete intersections and give the complete classification of threefold weighted complete intersections in weighted projective space that are canonically or anticanonically embedded.