论文标题
关于$ k $ wise的奇怪镇问题的注释
A note on $k$-wise oddtown problems
论文作者
论文摘要
对于整数$ 2 \ leq t \ leq k $，我们考虑了$ k $ set系列$ \ mathcal {a} _j：1 \ leq j \ leq k $ withy $ \ nathcal {a} a} _j = \ = \ \ \ \ \ {a___ {a} $ | a_ {1，i_1} \ cap \ cdots \ cap a_ {k，i_k} | $是何时且仅当$ i_j $的至少$ t $不同。在本文中，我们证明$ m = o（n^{1/\ lfloor k/2 \ rfloor}）$当$ t = k $和$ m = o（n^{1/（t-1}）$时，当$ 2T-2 \ leq k $时，这两个范围都可能是最大的。专门研究$ \ Mathcal {a} = \ Mathcal {a} _1 = \ cdots = \ Mathcal {a} _K $，我们恢复了经典奇怪的问题的变体。
For integers $2 \leq t \leq k$, we consider a collection of $k$ set families $\mathcal{A}_j: 1 \leq j \leq k$ where $\mathcal{A}_j = \{ A_{j,i} \subseteq [n] : 1 \leq i \leq m \}$ and $|A_{1, i_1} \cap \cdots \cap A_{k,i_k}|$ is even if and only if at least $t$ of the $i_j$ are distinct. In this paper, we prove that $m =O(n^{ 1/ \lfloor k/2 \rfloor})$ when $t=k$ and $m = O( n^{1/(t-1)})$ when $2t-2 \leq k$ and prove that both of these bounds are best possible. Specializing to the case where $\mathcal{A} = \mathcal{A}_1 = \cdots = \mathcal{A}_k$, we recover a variation of the classical oddtown problem.
