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- W1482165026 abstract "For two positive integers $n$ and $p$, let $mathcal{L}_{p}$ be the family of labeled $n$-sets given by $$mathcal{L}_{p}=big{{(1,ell_1),(2,ell_2),ldots,(n,ell_n)}: ell_iin[p], i=1,2ldots,nbig}.$$ Families $mathcal{A}$ and $mathcal{B}$ are said to be cross-intersecting if $Acap Bneqemptyset$ for all $Ain mathcal{A}$ and $Binmathcal{B}$. In this paper, we will prove that for $pgeq 4$, if $mathcal{A}$ and $mathcal{B}$ are cross-intersecting subfamilies of $mathcal{L}_{mathfrak{p}}$, then $|mathcal{A}||mathcal{B}|leq p^{2n-2}$, and equality holds if and only if $mathcal{A}$ and $mathcal{B}$ are an identical largest intersecting subfamily of $mathcal{L}_{p}$." @default.
- W1482165026 created "2016-06-24" @default.
- W1482165026 creator A5075975467 @default.
- W1482165026 date "2013-01-21" @default.
- W1482165026 modified "2023-10-11" @default.
- W1482165026 title "Cross-Intersecting Families of Labeled Sets" @default.
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- W1482165026 doi "https://doi.org/10.37236/3047" @default.
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