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- W4205977424 abstract "Let fm(a,b,c,d) denote the maximum size of a family F of subsets of an m-element set for which there is no pair of subsets A,B∈F with |A∩B|≥a,|Ā∩B|≥b,|A∩B̄|≥c,and|Ā∩B̄|≥d. By symmetry we can assume a≥d and b≥c. We show that fm(a,b,c,d) is Θ(ma+b−1) if either b>c or a,b≥1. We also show that fm(0,b,b,0) is Θ(mb) and fm(a,0,0,d) is Θ(ma). The asymptotic results are as m→∞ for fixed non-negative integers a,b,c,d. This can be viewed as a result concerning forbidden configurations and is further evidence for a conjecture of Anstee and Sali. Our key tool is a strong stability version of the Complete Intersection Theorem of Ahlswede and Khachatrian, which is of independent interest." @default.
- W4205977424 created "2022-01-25" @default.
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- W4205977424 date "2006-11-01" @default.
- W4205977424 modified "2023-09-27" @default.
- W4205977424 title "Pairwise intersections and forbidden configurations" @default.
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- W4205977424 doi "https://doi.org/10.1016/j.ejc.2006.05.002" @default.
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