Category Probabilistic Method

Discrepancy I

Consider a set system, a.k.a. hypergraph, where is the ground set and where . We wish to color the ground set $V$ with two colors, say red and blue, in such way that all sets in the family are colored in a  “balanced” way, i.e., each set has nearly the same number of red and blue points. […]

Distinct Sums

A set of positive integers is said to have distinct sums (DS) if all sums where   are distinct. We are interested in understanding the function .  We obtain a simple lower bound on by observing that the set  has DS as long as . Therefore, . Interestingly, this lower bound is not far away from being optimal, in […]

Giant component with Depth First Search

I just finished reading a short paper of Michael Krivelevich and Benny Sudakov, two leading experts in probabilistic combinatorics, which appeared in Arxiv about a month ago [1]. It is a simple proof of the classical result that the random binomial graph exhibits a phase transition around . When then the largest component has size […]