# Category Combinatorics

## 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 […]

## 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? […]