Related papers: Bounding, splitting, and almost disjointness
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.
We derive a family of necessary separability criteria for finite-dimensional systems based on inequalities for variances of observables. We show that every pure bipartite entangled state violates some of these inequalities. Furthermore, a…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
We investigate some properties of balayage, or, sweeping (out), of measures with respect to subclasses of subharmonic functions. The following issues are considered: relationships between balayage of measures with respect to classes of…
In this paper, we study the energy of semigraphs and obtain some bounds, and show that one of the bounds is tight. We also study the spectra of the adjacency matrix of a special type of rooted 3-uniform semigraph and enumerate those…
We study the separability of permutationally symmetric quantum states. We show that for bipartite symmetric systems most of the relevant entanglement criteria coincide. However, we provide a method to generate examples of bound entangled…
We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…
We obtain the generating functions for partial matchings avoiding neighbor alignments and for partial matchings avoiding neighbor alignments and left nestings. We show that there is a bijection between partial matchings avoiding three…
This paper investigates the a-posteriori analysis of Branch-and-Bound~(BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible…
The detection of entanglement in a bipartite state is a crucial issue in quantum information science. Based on realignment of density matrices and the vectorization of the reduced density matrices, we introduce a new set of separability…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
This paper considers three different partition relations from partition calculus, two of which are pair relations and one of which is a triple relation. An examination of the first partition relation and the ramification argument used to…
In the paper, the author derives several "diagonal" recurrence relations, constructs some inequalities, finds monotonicity, and poses a conjecture related to Stirling numbers of the second kind.
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…
We define the strong splitting number, prove that it equals s when exists, and put some restrictions on the possibility that s is a singular carcinal.
We study a correspondence between numerical sets and integer partitions that leads to a bijection between simultaneous core partitions and the integer points of a certain polytope. We use this correspondence to prove combinatorial results…
Bernoulli-$p$ thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences $(X_1,X_2,...)$; (2) gaps of such sequences $(X_{n+1}-X_1)_{n\in\mathbb{N}}$; (3) partition structures. For the first case…
Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp.…