Related papers: The generalized trifference problem

Linear statistics, a random variable build out of the sum of the evaluation of functions at the eigenvalues of a N times N random matrix,sum[j=1 to N]f(xj) or tr f(M), is an ubiquitous statistical characteristics in random matrix theory.…

We call a real multi-dimensional array a {\em tensor} for short. In enumerating vertices of the polytopes of stochastic tensors, different approaches have been used: {(1)} Combinatorial method via Latin squares; {(2)} Analytic (topological)…

We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system of PDE that involves unknown Lagrange multipliers and…

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied…

We prove polynomial upper bounds of geometric Ramsey numbers of pathwidth-2 outerplanar triangulations in both convex and general cases. We also prove that the geometric Ramsey numbers of the ladder graph on $2n$ vertices are bounded by…

There are numbers k and s and a URM program A(n,m) satisfying the following conditions. 1. If A(n,m) halts, then Cn(m) diverges. 2. For all n, C_k(n) = A(n,n) and C_s(n) = C_k(s). 3. A(k,s) halts and for all n, A(s,n) diverges. Here C_n(_)…

We address consecutively two problems. First we introduce a class of so called Fre'chet generalized controls for a multi-input control-affine system with non-commuting controlled vector fields. For each control of the class one is able to…

Let $\mathbb{S}_g$ be the orientable surface of genus $g$. We prove that the component structure of a graph chosen uniformly at random from the class $\mathcal{S}_g(n,m)$ of all graphs on vertex set $[n]=\{1,\dotsc,n\}$ with $m$ edges…

Truncated moment problems in the class of generalized Nevanlinna functions are investigated. General solvability criteria will be established, covering both the even and odd problems, including complete parametrizations of solutions. The…

The system of tensor equations (TEs) has received much considerable attention in the recent literature. In this paper, we consider a class of generalized tensor equations (GTEs). An important difference between GTEs and TEs is that GTEs can…

Products of $M$ i.i.d. random matrices of size $N \times N$ are related to classical limit theorems in probability theory ($N=1$ and large $M$), to Lyapunov exponents in dynamical systems (finite $N$ and large $M$), and to universality in…

A subset $Y$ of the general linear group $\operatorname{GL}(n,q)$ is called $t$-intersecting if $\operatorname{rk}(x-y)\le n-t$ for all $x,y\in Y$, or equivalently $x$ and $y$ agree pointwise on a $t$-dimensional subspace of…

Let $M$ be any compact four-dimensional PL-manifold with or without boundary (e.g. the four-dimensional sphere or ball). Consider the space $T(M)$ of all simplicial isomorphism classes of triangulations of $M$ endowed with the metric…

We consider string matching with variable length gaps. Given a string $T$ and a pattern $P$ consisting of strings separated by variable length gaps (arbitrary strings of length in a specified range), the problem is to find all ending…

An $m$-general set in $AG(n,q)$ is a set of points such that any subset of size $m$ is in general position. A $3$-general set is often called a capset. In this paper, we study the maximum size of an $m$-general set in $AG(n,q)$,…

The quadratic minimum spanning tree problem and its variations such as the quadratic bottleneck spanning tree problem, the minimum spanning tree problem with conflict pair constraints, and the bottleneck spanning tree problem with conflict…

In this paper we study the class of graphs $G_{m,n}$ that have the same degree sequence as two disjoint cliques $K_m$ and $K_n$, as well as the class $\overline G_{m,n}$ of the complements of such graphs. We establish various properties of…

Which graphs, in the class of all graphs with given numbers n and m of edges and vertices respectively, minimizes or maximizes the value of some graph parameter? In this paper we develop a technique which provides answers for several…

The problem of estimation error in portfolio optimization is discussed, in the limit where the portfolio size N and the sample size T go to infinity such that their ratio is fixed. The estimation error strongly depends on the ratio N/T and…

We study the principal bifurcation curve of a third order equation which describes the nonlinear evolution of several systems with a long--wavelength instability. We show that the main bifurcation branch can be derived from a variational…