AI 中文总结
针对满足偶两两交集条件的k元子集族，本文用Delsarte线性规划技术证明其大小上界，补充了Frankl与Tokushige指数级阈值外的相关结果。
AI 中文摘要
假设n=2m，k=2t且n>10k^7，我们证明：若n元集合的k元子集族F仅含偶两两交集，则|F|≤C(m,t)，且所有极值族均具有原子结构。此前Frankl与Tokushige已在n>n_FT(k)（n_FT(k)至少为指数级）时证明该结果，核心技术为Delsarte线性规划。
英文摘要
Suppose that $n=2m$, $k=2t$ and $n > 10 k^7$. We show that if a family $\mathcal F$ of $k$-subsets of an $n$-set has only even pairwise intersections then $|\mathcal F| \leq \binom{m}{t}$. Moreover, every extremal family has an atomic structure. This result was previously proved by Frankl and Tokushige for $n > n_{FT}(k)$, where $n_{FT}(k)$ is at least exponential. The main technique is Delsarte linear programming.
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