In this paper, we show that for any independence system, the problem of finding a persistency partition of the ground set and that of finding a maximum weight independent set are polynomially equivalent.

In this note, we study a constrained independent set problem for matroids and certain generalizations. The basic problem can be regarded as an ordered version of the matroid parity problem. By a reduction of this problem to matroid intersection, we prove a min-max formula. Studying the weighted case and a delta-matroid generalization, we prove that some of them are not more complex than matroid...

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

We investigate the effect of query rewriting on joins involving set-valued attributes in object-relational database management systems. We show that by unnesting set-valued attributes (that are stored in an internal nested representation) prior to the actual set containment or intersection join we can improve the performance of query evaluation by an order of magnitude. By giving example query ...

Consider a directed graph (digraph) in which vertices are assigned color sets, and two connected if only they share at least one the tail vertex has strictly smaller set than head. We seek to determine smallest possible size of union sets that allows for such digraph representation. To address this problem, we introduce new notion intersection representation digraph, show it is well-defined all...

We discuss two ways to determine, given I ⊂ S, whether I ∈ I. The first method is based on the previous lecture, where we considered the set Ŝ = ∪̇Ŝi, a union of disjoint copies of the Si. Formally, we write Ŝ = {(e, i) : e ∈ Si}. There is a natural mapping f : Ŝ → ∪Si which maps (e, i) to e. We can now define a partition matroid Mp over the ground set Ŝ, where I(Mp) = { I ⊆ Ŝ s.t. ∀e ∈ S : |I ∩...