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- W2618878438 abstract "Let K={k1,k2,…,kr} and L={l1,l2,…,ls} be disjoint subsets of {0,1,…,p−1}, where p is a prime and A={A1,A2,…,Am} is a family of subsets of [n]={1,2,…,n} such that |Ai|(modp)∈K for all Ai∈A and |Ai∩Aj|(modp)∈L for i≠j. In 1991, Alon, Babai and Suzuki conjectured that if n≥s+max1≤i≤rki, then |A|≤ns+ns−1+⋯+ns−r+1. In 2000, Qian and Ray-Chaudhuri proved the conjecture under the condition n≥2s−r. In 2015, Hwang and Kim verified this conjecture. In this paper, we will prove that if n≥2s−2r+1 or n≥s+max1≤i≤rki, then |A|≤n−1s+n−1s−1+⋯+n−1s−2r+1.This result strengthens both the upper bound of Alon–Babai–Suzuki’s conjecture and Qian and Ray-Chaudhuri’s result, when n≥2s−2." @default.
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- W2618878438 date "2018-01-01" @default.
- W2618878438 modified "2023-10-18" @default.
- W2618878438 title "A strengthened inequality of Alon–Babai–Suzuki’s conjecture on set systems with restricted intersections modulo p" @default.
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- W2618878438 doi "https://doi.org/10.1016/j.disc.2017.08.019" @default.
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