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- W2953256911 abstract "Let $K={k_1,k_2,ldots,k_r}$ and $L={l_1,l_2,ldots,l_s}$ be disjoint subsets of ${0,1,ldots,p-1}$, where $p$ is a prime and $A={A_1,A_2,ldots,A_m}$ be a family of subsets of $[n]$ such that $|A_i|pmod{p}in K$ for all $A_iin A$ and $|A_icap A_j|pmod{p}in L$ for $ine j$. In 1991, Alon, Babai and Suzuki conjectured that if $ngeq s+max_{1leq ileq r} k_i$, then $|A|leq {nchoose s}+{nchoose s-1}+cdots+{nchoose s-r+1}$. In 2000, Qian and Ray-Chaudhuri proved the conjecture under the condition $ngeq 2s-r$. In 2015, Hwang and Kim verified the conjecture of Alon, Babai and Suzuki. In this paper, we will prove that if $ngeq 2s-2r+1$ or $ngeq s+max_{1leq ileq r}k_i$, then [ |A|leq{n-1choose s}+{n-1choose s-1}+cdots+{n-1choose s-2r+1}. ] This result strengthens the upper bound of Alon, Babai and Suzuki's conjecture when $ngeq 2s-2$." @default.
- W2953256911 created "2019-06-27" @default.
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- W2953256911 date "2017-01-02" @default.
- W2953256911 modified "2023-09-26" @default.
- W2953256911 title "A strengthened inequality of Alon-Babai-Suzuki's conjecture on set systems with restricted intersections modulo p" @default.
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- W2953256911 doi "https://doi.org/10.48550/arxiv.1701.00585" @default.
- W2953256911 hasPublicationYear "2017" @default.
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