论文标题
Kruskal-Katona的功能和交叉交叉抗微生的变化
Kruskal-Katona's function and a variation of cross-intersecting antichains
论文作者
论文摘要
我们证明了Kruskal-Katona函数的某些特性，并适用于以下交叉交叉抗小选的变化。让$ n \ ge 4 $成为一个均匀的整数，$ \ mathscr {a} $和$ \ mathscr {b} $是两个交叉切断的抗抗抗，$ \ mathbb {n} _n $与最多$ k $ discoint in Cairs in \ in \ mathscr in \ a} $ in \ a} $ b_j \ in \ Mathscr {b} $，$ a_i \ cap b_j = \ emptyset $仅当$ i = j \ le k $时。我们证明，在$ | \ Mathscr {a} |+| \ Mathscr {B} | $上是最好的上限。此外，我们表明极端家族仅包含$ \ frac {n} {2} $和$（\ frac {n} {2} {2} +1）$ - sets。
We prove some properties of the Kruskal-Katona function, and apply to the following variation of cross-intersecting antichains. Let $n\ge 4$ be an even integer and $\mathscr{A}$ and $\mathscr{B}$ be two cross-intersecting antichains of $\mathbb{N}_n$ with at most $k$ disjoint pairs, i.e. for all $A_i\in \mathscr{A}$, $B_j\in\mathscr{B}$, $A_i\cap B_j=\emptyset$ only if $i=j\le k$. We prove a best possible upper bound on $|\mathscr{A}|+|\mathscr{B}|$. Furthermore, we show that the extremal families contain only $\frac{n}{2}$ and $(\frac{n}{2}+1)$-sets.
