ZichaoDong

For $\boldsymbol{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb F}_2^k$, an $\boldsymbol{\alpha} $-town is a set family in which every $i$-wise intersection has parity $\alpha_i$. Denote by $f_{\boldsymbol{\alpha} }(n)$ the maximum size of an $\boldsymbol{\alpha} $-town on $$. The classical oddtown and eventown problems study the cases $\boldsymbol{\alpha} = (1, 0)$ and $(0, 0)$, respectively. We …