Old and New Results for the Weighted t-Intersection Problem via AK-Methods
Old and New Results for the Weighted t-Intersection Problem via AK-Methods
复制标题
通过 AK 方法求解加权 t 交点问题的新旧结果
DOI：
10.1007/978-1-4757-6048-4_5
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
K. Engel
中科院分区：
文献类型：
--
作者：
Christian Bey;K. Engel
Let [n]: = {1, ..., n}, 2[n] be the power set of [n] and s ∈ [n]. A family F ⊆ 2[n] is called t-intersecting in [s] if
$$\left| {{X_1} \cap {X_2} \cap \left[ s \right]} \right| \geqslant t\,for\,all\,{X_1},{X_2}\, \in \,F.$$
Let ω: 2[n] → ℝ+ be a given weight function and
$${M_s}\left( {n,t;\omega } \right):\, = \max \left\{ {\omega \left( F \right)} \right.:F\,is\,t - \operatorname{int} er\sec ting\,in\left. {\,\left[ s \right]} \right\}.$$
For several weight functions, the numbers M n (n, t; ω) can be determined using three important methods of Ahlswede and Khachatrian: Generating Sets [2], Comparison Lemma [4], and Pushing-Pulling [3]. We survey these methods.
Let [n]: = {1, ..., n}, 2[n] be the power set of [n] and s ∈ [n]. A family F ⊆ 2[n] is called t-intersecting in [s] if
$$\left| {{X_1} \cap {X_2} \cap \left[ s \right]} \right| \geqslant t\,for\,all\,{X_1},{X_2}\, \in \,F.$$
Let ω: 2[n] → ℝ+ be a given weight function and
$${M_s}\left( {n,t;\omega } \right):\, = \max \left\{ {\omega \left( F \right)} \right.:F\,is\,t - \operatorname{int} er\sec ting\,in\left. {\,\left[ s \right]} \right\}.$$
For several weight functions, the numbers M n (n, t; ω) can be determined using three important methods of Ahlswede and Khachatrian: Generating Sets [2], Comparison Lemma [4], and Pushing—Pulling [3]. We survey these methods.