Pre-Q&A

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
Congrats, everyone!

agentredlum said:
If you get it to {0 ... 9} AND CRG is correct that this is an open question then you should become famous.
Hopefully the paper (not mine!) will come out soon and we'll have some verification on the current state-of-the-art. I think that they proved that you need at least one coefficient >= 5, but don't trust that until I can check my notes. Apparently my memory is untrustworthy. :D

OK, next person to post a question has it!
 

mathbalarka

Math Team
Mar 2012
3,871
86
India, West Bengal
CRGreathouse said:
Congrats, everyone!
Wait! What was your solution? Is 11 the minimum degree for h?
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
mathbalarka said:
Wait! What was your solution
I don't have it here, but I'll post it Monday afternoon.

mathbalarka said:
Is 11 the minimum degree for h?
I think my example was degree 10.

There should be a minimum degree for solutions with max coefficient 10, and another minimum degree for solutions with any coefficients. Proving what they are for the case 2 that I picked is hard. I think the other cases are easier (and some results there have been proved).
 

mathbalarka

Math Team
Mar 2012
3,871
86
India, West Bengal
CRGreathouse said:
Proving what they are for the case 2 that I picked is hard.
Gimme a hint on how to prove it.

CRGreathouse said:
OK, next person to post a question has it!
I give control to any one who wants to post.
 

agentredlum

Math Team
Jul 2011
3,372
234
North America, 42nd parallel
I suggest we start another Q&A thread but keep this one open (and in mind) for our current discussions.

Thank you for your considerations in this matter.

Your's Truly,
agentredlum
 

mathbalarka

Math Team
Mar 2012
3,871
86
India, West Bengal
I vote for keeping the Q&A here. This is just a pre-version so we might not want to mix up the upcoming real version with it. Anyways, who wants to pose the next problem? I have nothing in my bag :p
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
agentredlum said:
I suggest we start another Q&A thread but keep this one open (and in mind) for our current discussions.
mathbalarka said:
I vote for keeping the Q&A here. This is just a pre-version so we might not want to mix up the upcoming real version with it.
Fine by me. This was just a stopgap, but if you're enjoying it...

mathbalarka said:
Anyways, who wants to pose the next problem? I have nothing in my bag :p
My plan was that (for this pre-thread) anyone could jump in and post questions, regardless of whether they -- or anyone! -- had solved the last question.

With that said, I'll try to post one soon.
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
mathbalarka said:
CRGreathouse said:
Proving what they are for the case 2 that I picked is hard.
Gimme a hint on how to prove it.
It's an open problem since at least 1984. Cole-Dunn-Filaseta don't solve it (well, not as of last month anyway :D). Current bounds are 5 to 9: no examples with coefficients 0..5 exist, and examples with coefficients 0..10 are known.
 

CRGreathouse

Forum Staff
Nov 2006
16,046
936
UTC -5
Q2. Consider the n X n boards here: viewtopic.php?f=40&t=46118 and let a(n) be the minimum value of the largest number on such an n X n board. What are the asymptotics of a(n)?

I have no idea if this is moderately easy or excruciatingly hard.

Bonus: Why is this not in the OEIS?