2 research outputs found
Forbidding a Set Difference of Size 1
How large can a family \cal A \subset \cal P [n] be if it does not contain
A,B with |A\setminus B| = 1? Our aim in this paper is to show that any such
family has size at most \frac{2+o(1)}{n} \binom {n}{\lfloor n/2\rfloor }. This
is tight up to a multiplicative constant of . We also obtain similar results
for families \cal A \subset \cal P[n] with |A\setminus B| \neq k, showing that
they satisfy |{\mathcal A}| \leq \frac{C_k}{n^k}\binom {n}{\lfloor n/2\rfloor
}, where C_k is a constant depending only on k.Comment: 8 pages. Extended to include bound for families \cal A \subset \cal P
[n] satisfying |A\setminus B| \neq k for all A,B \in \cal