2026.07.21, Zichao Dong, k-wise odd-even towns

Zichao Dong, k-wise odd-even towns July 21 Tuesday @ 4:30 PM - 5:30 PM KST Room B332, IBS (기초과학연구원) Zichao Dong IBS Extremal Combinatorics and Probability Group https://dzch0310.github.io/dzch0310/ 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 $[n]$. The classical oddtown and eventown problems study the cases $\boldsymbol{\alpha} = (1, 0)$ and $(0, 0)$, respectively. We determine the sharp asymptotics of $f_{\boldsymbol{\alpha} }(n)$ for all $\boldsymbol{\alpha} $, answering questions of Johnston-O’Neill and Wei-Zhang-Ge.