For Bollobás systems of d-tuples, the conjectured bound sum of inverse multinomials <= 1 is false; the paper proves an asymptotically tight upper bound for d=3 and tight uniform skew bounds.
Heged¨ us, A Bollob´ as-type theorem for affine subspaces, Australasian Journal of Com- binatorics 63 (2015) 262-267
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On Bollob\'as-type theorems of $d$-tuples
For Bollobás systems of d-tuples, the conjectured bound sum of inverse multinomials <= 1 is false; the paper proves an asymptotically tight upper bound for d=3 and tight uniform skew bounds.