Sharp bounds on $k$-wise generalizations of oddtowns and eventowns

Zichao Dong, Minghui Ouyang, Lan Wei

For $\mathbf{\alpha }=({\alpha }_1,\dots ,{\alpha }_k)\in {\mathbb{F}}_2^k$, an $\mathbf{\alpha }$-town is a set family in which every $i$-wise intersection has parity ${\alpha }_i$. Denote by $f_{\boldsymbolα}…