相关论文: Minimal length maximal green sequences
In this paper we present novel algorithms for several multidimensional data processing problems. We consider problems related to the computation of restricted clusters and of the diameter of a set of points using a new distance function. We…
Attending to an open problem in the literature stated by Mirzakhani and Vondr\'ak, we give a lower bound of the number of non-monochromatic simplices for Sperner labelings of the vertices of a triangulation of a given $ k$-simplex with…
The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's…
We introduce a class of models of semiflexible polymers. The latter are characterized by a strong rigidity, the correlation length associated to the gradient-gradient correlations, called the persistence length, being of the same order as…
The covering type of a space $X$ is defined as the minimal cardinality of a good cover of a space that is homotopy equivalent to $X$. We derive estimates for the covering type of $X$ in terms of other invariants of $X$, namely the ranks of…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
Over some types of trees with a given number of vertices, which trees minimize or maximize the total number of subtrees or leaf containing subtrees are studied. Here are some of the main results:\ (1)\, Sharp upper bound on the total number…
We study minimal vertex covers and maximal matchings on trees. We pay special attention to the corresponding backbones i.e. these vertices that are occupied and those that are empty in every minimal vertex cover (resp. these egdes that are…
Suppose $\mathcal{X}$ is an $n$-correct set of nodes in the plane, that is, it admits a unisolvent interpolation with bivariate polynomials of total degree less than or equal to $n.$ Then an algebraic curve $q$ of degree $k\le n$ can pass…
The cyclic matching sequenceability of a simple graph $G$, denoted $\mathrm{cms}(G)$, is the largest integer $s$ for which there exists a cyclic ordering of the edges of $G$ so that every set of $s$ consecutive edges forms a matching. In…
In two recent papers, a new method was developed for calculating ten-dimensional superstring amplitudes with an arbitrary number of loops and external massless particles, and for expressing them in manifestly Lorentz-invariant form. By…
Recently a systematic investigation of monoids of sequences of plus-minus weighted zero-sum sequences had been started, which is among others motivated by applications to monoids of norms of algebraic integers. In the current paper these…
This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory…
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…
Given a contractive tuple of Hilbert space operators satisfying certain $A$-relations we show that there exists a unique minimal dilation to generators of Cuntz-Krieger algebras or its extension by compact operators. This Cuntz-Krieger…
\emph{A maximal distance minimizer} for a given compact set $M \subset \mathbb{R}^2$ and some given $r > 0$ is a set having the minimal length (one-dimensional Hausdorff measure) over the class of closed connected sets $\Sigma \subset…
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…
Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
Recent articles have shown the connection between representation theory of quivers and the theory of cluster algebras. In this article, we prove that some cluster algebras of type ADE can be recovered from the data of the corresponding…
We study limits of convergent sequences of string graphs, that is, graphs with an intersection representation consisting of curves in the plane. We use these results to study the limiting behavior of a sequence of random string graphs. We…