##### Department of Mathematics,

University of California San Diego

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### ABACUS

## Jason O'Neill

#### University of California, San Diego

## Towards supersaturation for oddtown and eventown

##### Abstract:

In an $n$-resident town, Oddtown, all of their clubs must satisfy the following properties: all clubs must have an odd number of members and amongst any two distinct clubs, there must be an even number of residents in common. The classical oddtown theorem states that any such town can have at most $n$ clubs. In this talk, we explore how the residents can have $n+1$ clubs of odd size and minimize the chance of the town catching them. That is, we'd like to minimize the number of pairs of clubs with an odd number of members in common. We will also explore a similar problem with Eventown.

### October 5, 2021

### 12:30 PM

Zoom -- email jmoneill@ucsd.edu for link

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