Category Mathematics
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 […]
The Ballot Theorem
Today’s post is going to be about politics. Consider an election where there are two candidates, call them A and B, who receive votes respectively, and let us assume that . Assume that all possible “trajectories” are equally likely. What is the probability that candidate B is ahead of A throughout the vote counting procedure? […]
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