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A note on Snevily's conjecture in set systems
Rudy X. J. Liu,황경원,김연진 장전수학회 2017 Advanced Studies in Contemporary Mathematics Vol.27 No.1
Let L = {l1, l2, . . . , ls} be a set of s nonnegative integers and K = {k1, k2, . . . , kr} be a set of integers satisfying max lj < min ki. Let F be an L-intersecting family of subsets of {1, 2, . . . , n} such that |F| ∈ K for every F ∈ F. Let {0, 1, . . . , s - r - 1} ⊆ L with 1 < r < s and K be any set of integers with min ki > s - r and K ∩ L = Ø. Then |F| ≤ (n-1s)+(n-1s-1)+…+(n-1s-r). These results conrm Snevily's conjecture on set systems partially.