Timeline for How many rich directions does a set in $\mathbb F_p^2$ determine?

11 events

when toggle format	what		by	license	comment
S Jun 6, 2018 at 3:53	history	suggested	Luca Ghidelli	CC BY-SA 4.0	Added relevant reference
Jun 6, 2018 at 2:20	review	Suggested edits
S Jun 6, 2018 at 3:53
May 4, 2018 at 20:43	history	edited	Seva	CC BY-SA 4.0	added 145 characters in body
May 3, 2018 at 15:56	history	edited	Seva	CC BY-SA 4.0	added 234 characters in body; edited title
May 2, 2018 at 5:37	comment	added	Seva		@NoamD.Elkies: any range $(2-\epsilon)p<\|P\|\le 2p$ with $\epsilon>0$ fixed is fine for my purposes.
May 2, 2018 at 5:15	answer	added	Luca Ghidelli		timeline score: 3
May 2, 2018 at 4:44	comment	added	Luca Ghidelli		For p=7 and \|P\|=14 it is even possible to have only 5=p-2 rich directions! With the following construction: P'={(0,k): k\in F_7}\cup{(k,0): k\in F_7}, P=P'\cup{(5,5),(5,6),(6,5)}. It looks like the optimal values interpolates the function (p+3)/2...
May 2, 2018 at 4:39	comment	added	Luca Ghidelli		For p>3 and \|P\|=2p it is possible to have only \|P\|-p-1=p-1 rich directions, with the following construction: P'={(h,k): h\in{0,1} k\in F_p}, P=P'\cup{(-1,0),(2,2)}\setminus{(0,0),(2,1)}.
May 1, 2018 at 21:04	comment	added	Noam D. Elkies		Why $\frac53$ ?
May 1, 2018 at 18:48	history	edited	Seva	CC BY-SA 3.0	added 31 characters in body
May 1, 2018 at 17:47	history	asked	Seva	CC BY-SA 3.0