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Thread: New Project - Van Der Waerdon Numbers

  1. #1
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    New Project - Van Der Waerdon Numbers

    Link to home page is here: http://www.vdwnumbers.org/vdwnumbers/index.php

    Link to team page is here: http://www.vdwnumbers.org/vdwnumbers....php?teamid=11

    Van Der Waerden Numbers is a research project that uses Internet-connected computers to find better lower bounds for these numbers. You can participate by downloading and running a free program that runs on your computer when you're not using it. To participate, Download and run BOINC, and add Project 'vdwnumbers.org/vdwnumbers/' (for Windows computers only, does not work with Avast). You can also Read our rules and policies. This is a project of Daniel Monroe, who is a student at Takoma Park Middle School.

    Background

    The sequence of colors BRRBBRRB (where B is blue and R is red) does not have an evenly spaced subsequence of length 3 that are the same color. However, if you add a B to the end, you get BRRBBRRBB, which has the same color blue in positions 1,5, and 9 which are evenly spaced 4 apart. If you add an R to the end, you get BRRBBRRBR, which has R at position 3, 6, and 9. In fact, with only two colors, there is no sequence of length 9 of Bs and Rs that does not have a subsequence of 3 evenly spaced of the same color. Van der Waerden's Theorem states that for any number of colors r and length k, a long enough sequence always has an evenly spaced subsequence of the same color. The smallest length guaranteed to have an evenly spaced subsequence is called the Van Der Waerden Number and is written W(k,r). For example, W(3,2)=9. This project is to find better lower bounds for Van Der Waerden Numbers by finding sequences like BRRBBRRB. See a table of the results so far below.





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  2. #2
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    NeoGen is offline AMD Users Alchemist Moderator
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  3. #3
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    Quote Originally Posted by NeoGen View Post
    I'm in there with you Nflight!
    Me too!

    P.S. Notice that the thread name is not the same as the project name - Van Der Waerden Numbers


  4. #4
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    NeoGen is offline AMD Users Alchemist Moderator
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    For me who don't know the origins of the name or the original language (sounds like dutch though) it looks hard to spell, or even pronounce... can we just call it "Weird numbers"? Unfortunately that name is already taken...
    Last edited by NeoGen; 03-11-2015 at 04:20 AM.

  5. #5
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    Bartel Leendert van der Waerden, the man behind Van der Waerden's theorem -which leads to the search for Van der Waerden numbers- was indeed Dutch.


  6. #6
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    Urrggghhh!! Yet another project to dilute my GHz. Crikey I haven't finished 1M in Universe yet.

  7. #7
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    Quote Originally Posted by vaughan View Post
    Urrggghhh!! Yet another project to dilute my GHz. Crikey I haven't finished 1M in Universe yet.
    Now that is a clear goal: Ye olde planet Dirt itself!


  8. #8
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    Welcome to the Team their AMDave, and low and behold if Dirk would turn on some boxen we might be able to maintain #1 PLACE overall. RAC and overall Points we have the 1st Place position. I Have my whole system working like mad in trying to keep us right there! I am about to hit 10K but I am not stopping there heading on up to 100K so I have a few more days of crunching ahead of me!





    Challenge me, or correct me, but don't ask me to die quietly.

    …Pursuit is always hard, capturing is really not the focus, it’s the hunt ...

  9. #9
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    I'll be polishing my NFS 15e badge for the next five days -all 14e WUs error out.
    After the NFS challenge I'll give Van der Waerden (pronounce it just like Van der Waarden) a boost...
    Last edited by Dirk Broer; 03-15-2015 at 12:07 AM.


  10. #10
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    Such a spitting and carrying on, I am now getting more computation error then completed units. Time to go back to Poem@home until they work out this bug, and it was going so well. You need to babysit the project every 90 minutes or you can waste precious time in your other projects you have open and lose a position in the world domination position. RATS or as Vaughan calls it Crikkey!

    139 reporting only 4 were completed tasks! That sux!
    Last edited by Nflight; 03-15-2015 at 05:09 PM. Reason: Added words





    Challenge me, or correct me, but don't ask me to die quietly.

    …Pursuit is always hard, capturing is really not the focus, it’s the hunt ...

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