Cross-Intersecting Families of Labeled Sets

[摘要] For two positive integers $n$ and $p$, let $\mathcal{L}_{p}$ be the family of labeled $n$-sets given by $$\mathcal{L}_{p}=\big\{\{(1,\ell_1),(2,\ell_2),\ldots,(n,\ell_n)\}: \ell_i\in[p], i=1,2\ldots,n\big\}.$$ Families $\mathcal{A}$ and $\mathcal{B}$ are

[学科分类] 离散数学和组合数学

[关键词] EKR theorem;Intersecting family;cross-intersecting family;labeled set