A few new oddtown and eventown problems

Griffin Johnston, Jason O'Neill

Given a vector $\hat{I}\pm =(\hat{I}{\pm }_1,\dots ,\hat{I}{\pm }_k)\in {\mathbb{F}}_2^k$, we say a collection of subsets $\mathcal{F}$ satisfies $\hat{I}\pm$-intersection pattern modulo $2$ if all $i$-wise intersecti…