A note on Snevily's conjecture in set systems
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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 con rm Snevily's conjecture on set systems partially.
Abstract
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 con rm Snevily's conjecture on set systems partially.
참고문헌 (6)
- N. Alon, "Multilinear polynomials and Frankl-Ray-Chaudhuri-Wilson-Type intersection theorems", J. Combinatorial Theory, Ser. A, 58, pp.165~180 (1991)
- D. K. Ray-Chaudhuri, "On t-designs", Osaka J. Math, 12, pp.737~744 (1975)
- William Y. C. Chen, "Set systems with L-intersections modulo a prime number", J. Combinatorial Theory, Ser. A, 116, pp.120~131 (2009)
- K. W. Hwang, "Intersection families and Snevily's conjecture", European Journal of Combinatorics, 28, pp.843~847 (2007)
- Hunter S. Snevily, "On generalizations of the deBruijin-Erdos theorem", J. Combinatorial Theory, Ser. A, 68, pp.232~238 (1994)
- Hunter S. Snevily, "A generalization of the Ray-Chaudhuri and Wilson theorem", J. Combinatorial De-sign, 3, pp.349~352 (1995)