# Almost eventown

Let $n$ be an even positive integer. An eventown is a collection of subsets of $\{1,\ldots,n\}$ with the property that every two not necessarily distinct elements have even intersection. Berlekamp determined the largest size of an even town in the 1960s, answering a question of Erdős. In line with other Erdős questions, Ahmadi and Mohammadian made a conjecture on the size of the largest size of an almost eventown: a family of subsets of $\{1,\ldots,n\}$ with the property that among any three elements there are two with even intersection. In this talk we will prove the conjecture and mention other related results proved in joint work with Ali Mohammadi.

Giorgis Petridis