A central problem in extremal graph theory is to estimate, for a given graph $H$, the number of $H$-free graphs on a given set of $n$ vertices. In the case when $H$ is not bipartite, fairly precise… Expand

Let M be an n × m matrix of independent Rademacher (±1) random variables. It is well known that if n ≤ m, then M is of full rank with high probability. We show that this property is resilient to… Expand

We describe a construction of PRGs from one way permutations. Later, we discuss discuss why we need a permutation as opposed to any one way function. Here is a very natural approach to try and… Expand

We derive asymptotic formulas for the number of integer partitions with given sums of jth powers of the parts for j belonging to a finite, non-empty set J ⊂ N. The method we use is based on the… Expand

We show that if $W$ is allowed to approach 1 at a finite number of points, and displays moderate rate of growth near these points, then the clique number of $\mathbb{G}(n,W)$ will be $\Theta(\sqrt{n})$ almost surely.Expand