Math 270: Interlacing Families Open Problems

An Interlacing Result on Normalized Laplacians

Interleaving area problems in the 4th grade classroom: What is the role of context and practice?

Typical mathematics instruction involves blocked practice across a set of conceptually similar problems. Interleaving, or practice across a set of conceptually dissimilar problems, improves learning and transfer by repeatedly reloading information and increasing discrimination of problem features. Similarly, comparing problems across different contexts highlights relevant and irrelevant knowled...

Separating hash families: A Johnson-type bound and new constructions

Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory, we solve several open problems and conjectures concerning bounds and constructions for separating hash families. Firstly, we discover that the cardinality of ...

The Number of Interlacing Equalities Resulting from Removal of a Vertex from a Tree

We consider the set of Hermitian matrices corresponding to a given graph, that is, Hermitian matrices whose nonzero entries correspond to the edges of the graph. When a particular vertex is removed from a graph a number of eigenvalues of the resulting principal submatrix may coincide with eigenvalues of the original Hermitian matrix. Here, we count the maximum number of “interlacing equalities”...

On some open problems in cone metric space over Banach algebra

In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...