Related papers: Tripartite Unions
On objects of a triangulated category with a stability condition, we construct a topology.
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…
In this note we give a wellfoundedness proof of a computable notation system for first-order reflection.
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
Let $X,Y,Z$ and $W$ be normed spaces and $f:X\times Y\times Z\longrightarrow W $ be a bounded tri-linear mapping. In this Article, we define the topological centers for bounded tri-linear mapping and we invistagate thier properties. We…
Any smooth projective curve embeds into $\mathbb{P}^3$. More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a threefold $X$, then $X$ is…
In this purely experimental work we try to represent the set of plane maps with 3 vertices and 3 faces as a bipartite ribbon graph. In particular, this construction allows one to estimate the genus of the initial set.
Multipartite entanglement is a key resource for various quantum information tasks. Here, we present a scheme for generating genuine tripartite entanglement via nonlinear optical processes. We derive, in the Fock basis, the corresponding…
We show upper and lower bounds for angles in iterations of trisections of certain triangulations.
We provide a lower bound construction showing that the union of unit balls in three-dimensional space has quadratic complexity, even if they all contain the origin. This settles a conjecture of Sharir.
We give a criterion for cohomological symmetry in a triangulated category. As an application, we show that such cohomological symmetry holds for all pairs of modules over any exterior algebra.
We present the generalization of the entanglement of formation for three-party systems in a pure state. For three qubit system we derive out its explicit and closed expression which is a linear combination of the binary entropy functions…
In this note we show that the union of $r$ general lines and one fat line in ${\mathbb P}^3$ imposes independent conditions on forms of sufficiently high degree $d$, where the bound on $d$ is independent of the number of lines. This extends…
A classification is given of all the countable homogeneous ordered bipartite graphs.
In this work, we show that for a certain class of threefolds in positive characteristics, rational-chain-connectivity is equivalent to supersingularity. The same result is known for K3 surfaces with elliptic fibrations. And there are…
We prove a new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian. This condition is most easily described as a property of the dual graph. Let $G$ be a planar triangulation. Then the dual $G^*$ is a cubic…
This article gives a foundational account of various characterizations of framed links in the $3$-sphere.
This paper's central theme is to prove the existence of an n-algebra whose multiplication cannot be expressed employing any binary operation. Furthermore, to prove if two algebras are not isomorphic, this property does not hold for…
We show that the triple-crossing number of any knot is greater or equal to twice its (canonical) genus and we show an even stronger bound in the case of links. As an application we show that this bound is strong enough to obtain the…