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MIT PRIMES/Art of Problem Solving

CROWDMATH 2016: Pattern Avoidance

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Pattern Avoidance J
Problem 9 Important Results
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iamgauss
301 posts
#1 • 2 Y
This topic is linked to Problem 9.
Y by Adventure10, Mango247
As you may know, there is a thread for Problem 7 that lists all the important results discovered by CrowdMath for that problem. I thought it might be helpful to have a similar thread for the rest of the problems. Please add all important discoveries that have been made that are topical to Problem 9 here. Make sure to say where the theorems were proved and by whom. There are also threads for Problems 1-8. Thanks!
This post has been edited 2 times. Last edited by iamgauss, Apr 30, 2016, 4:05 PM
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iamgauss
301 posts
#2 • 2 Y
Y by Adventure10, Mango247
Please do not add any "thoughts in progress" here, but instead post them on a new thread, a problem-specific thread, or the "New Ideas and Theorems" thread if they do not appear to have any applications right now. Thanks!
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abk2015
3265 posts
#3 • 1 Y
Y by Adventure10
To solve this problem, we just have to differentiate the energy with respect to the function and set it equal to zero. This should provide either a minima or a maxima which would go a long way towards the solution of the problem (possibly it could even solve it).
This post has been edited 1 time. Last edited by abk2015, Apr 30, 2016, 4:26 PM
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iamgauss
301 posts
#4 • 2 Y
Y by Adventure10, Mango247
I was actually intending for this thread to contain already proved results; could you post this in "New Ideas and Theorems" instead? Thanks!
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vkmathwhiz
1 post
#5 • 2 Y
Y by Adventure10, Mango247
These are a little too hard...
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Problem 9 Important Results
iamgauss   4
N Jan 11, 2019 by vkmathwhiz
As you may know, there is a thread for Problem 7 that lists all the important results discovered by CrowdMath for that problem. I thought it might be helpful to have a similar thread for the rest of the problems. Please add all important discoveries that have been made that are topical to Problem 9 here. Make sure to say where the theorems were proved and by whom. There are also threads for Problems 1-8. Thanks!
4 replies
iamgauss
Apr 29, 2016
vkmathwhiz
Jan 11, 2019
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CrowdMath Problems 8 and 9
JGeneson   17
N May 10, 2016 by JGeneson
Using a computer will help to search for optimal codes and universally optimal codes in problems 8 and 9. If you know Python, here is some code to help you start searching.

If you see any bugs in the code or have any questions about how it works, please let me know.
17 replies
JGeneson
Mar 4, 2016
JGeneson
May 10, 2016
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Problem 9 Important Results
iamgauss   4
N Jan 11, 2019 by vkmathwhiz
As you may know, there is a thread for Problem 7 that lists all the important results discovered by CrowdMath for that problem. I thought it might be helpful to have a similar thread for the rest of the problems. Please add all important discoveries that have been made that are topical to Problem 9 here. Make sure to say where the theorems were proved and by whom. There are also threads for Problems 1-8. Thanks!
4 replies
iamgauss
Apr 29, 2016
vkmathwhiz
Jan 11, 2019
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