tag:blogger.com,1999:blog-3722233.post7077840493326820837..comments2021-12-06T22:20:37.890-06:00Comments on Computational Complexity: New Ramsey Result that will be hard to verify but Ronald Graham thinks its right which is good enough for me.Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-3722233.post-13993340680928339012016-06-05T01:03:05.444-05:002016-06-05T01:03:05.444-05:00Egdiroh- I looked back at the paper and I had tran...Egdiroh- I looked back at the paper and I had transposed<br />digits in the result. I have made the correction.<br />Thanks for catching the mistake!<br />Apologies.<br /><br />GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-15210513255296244802016-06-04T19:11:24.096-05:002016-06-04T19:11:24.096-05:00This was this list I referenced. http://www.tsm-re...This was this list I referenced. http://www.tsm-resources.com/alists/PythagTriples.txtEgdirohhttps://www.blogger.com/profile/13330546489241723302noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-9534772001409849642016-06-04T19:10:01.112-05:002016-06-04T19:10:01.112-05:00x,y,z in {1,...,n} right? So if f( c) is 7285. The...x,y,z in {1,...,n} right? So if f( c) is 7285. Then there exists 2 coloring of {1,...,7284} in which there are not same colored (x,y,z), because 7285 is the least such n. Call that coloring C'. There are two colorings of {1,...,7285} that are identical to C' for {1,...,7284}. We can call those C'+black and C'+white. because f( c) = 7285 those colorings both contain monochromatic solutions. If either of them doesn't use 7285 as z then C' had a monochromatic solution. so it must be the case that there exist (x1, y1) white in C' and (x2, y2) black in C` such that x1^2 + y1^2 = 7285^2 = x2^2 + y2^2. Otherwise one of those colorings does not have a monochromatic (x,y,z). Now the table I looked at said that 7285 was only in one such triple of integers. So either the table I referenced is wrong. My understanding of f( c) is still wrong. You've transcribed the result incorrectly and it's some other number. or their result is wrong. Egdirohhttps://www.blogger.com/profile/13330546489241723302noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-26261219549684001412016-06-04T13:12:19.223-05:002016-06-04T13:12:19.223-05:00You misread my definition of f(c), which had a ......You misread my definition of f(c), which had a ... in it so perhaps it was unclear on my part. Here is the full definition:<br /><br />f(c) is the least n such that for any c-coloring of {1,...n} there<br />exists x,y,z all the same color such that x^2 + y^2 = z^2.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-37588625347652494292016-06-04T09:35:17.271-05:002016-06-04T09:35:17.271-05:00I went to build the graph of related triples so th...I went to build the graph of related triples so that I could see this in action, and in the triples dataset I was looking at there was only 1 pair (x,y) such that x^2 + y^2 = 7285. But if that is true either you gave wrote down the wrong value for f(2) or defined it wrong, or that's not it's value, or I'm just really confused by what you were trying to say. Because for 7285 to be least n, Then there most be a coloring of {1,...,7284} with no monochrome solution, but for which both of the related colorings of {1,...,7285} have a monochrome solution. But that would require 2 solutions to x^2 + y^2 = 7285. So there is something that is incorrect. Egdirohhttps://www.blogger.com/profile/13330546489241723302noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-46189888665740253672016-06-02T08:24:30.891-05:002016-06-02T08:24:30.891-05:00If there is a typo in the above post let me know a...If there is a typo in the above post let me know and<br />I will correct it.GASARCHhttps://www.blogger.com/profile/06134382469361359081noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-59793970600916345332016-06-01T22:46:28.702-05:002016-06-01T22:46:28.702-05:00You should read your posts after you post them to ...You should read your posts after you post them to catch typos.Anonymousnoreply@blogger.com