How large can a family A@?P[n] be if it does not contain A,B with |A@?B|=1? Our aim in this paper is to show that any such family has size at most 2+o(1)n(n@?n/2@?). This is tight up to a multiplicative constant of 2. We also obtain similar results for families A@?P[n] with |A@?B| k, showing that they satisfy |A|@?C"kn^k(n@?n/2@?), where C"k is a constant depending only on k.
['Imre Leader', 'Eoin Long']
Forbidding a set difference of size 1