Timeline for Set system with different differences

10 events

when toggle format	what		by	license	comment
Dec 12, 2015 at 6:39	history	edited	Daniel Soltész		edited tags
Jul 24, 2014 at 16:03	history	edited	Daniel Soltész		edited tags
Jun 3, 2014 at 22:28	answer	added	t3suji		timeline score: 6
Jun 3, 2014 at 22:08	answer	added	Kellen Myers		timeline score: 4
Jun 3, 2014 at 20:33	comment	added	Daniel Soltész		@eins6180 A little better but still simple upper bound would be that all the $2 \binom{\|\mathcal{A}\|}{2}$ differences are different so there can not be more than $2^n$ of them which means that $\|\mathcal{A}\|$ can not be asymptotically bigger than $2^{n/2}$.
Jun 3, 2014 at 20:26	comment	added	eins6180		Here is a simple and probably much too large upper bound: Any maximal antichain in the lattice of all subsets of $[n]$ together with two other subsets doesn't work. So the family $\mathcal{A}$ cannot be bigger than ${n \choose [n/2]} + 1$.
Jun 3, 2014 at 20:20	comment	added	Daniel Soltész		@Seva Nice construction, you can also add [1,m] and [m+1,n] to obtain a system of $\lfloor n/2 \rfloor +2$ elements.
Jun 3, 2014 at 19:52	comment	added	Seva		Constructing $m:=\lfloor n/2\rfloor$ sets is easy: assuming that the ground set is $[1,n]$, take $A_i:=\{i\}\cup[m+1,n]\setminus\{m+i\}\ (1\le i\le m)$.
Jun 3, 2014 at 19:37	history	edited	Daniel Soltész	CC BY-SA 3.0	added 1 character in body
Jun 3, 2014 at 18:04	history	asked	Daniel Soltész	CC BY-SA 3.0