24小时热门版块排行榜

返回列表

当前主题已经存档。

formleaf

木虫 (正式写手)

应助: 0 (幼儿园)
贵宾: 1.097
金币: 3383.1
散金: 2780
红花: 3
帖子: 991
在线: 69.6小时
虫号: 698652
注册: 2009-02-09
性别: GG
专业: 组合数学

[交流] 【转帖】陶哲轩博客上的一篇新作

看到的陶哲轩博客上最近的一篇新作，不是很明白，贴出来大家看看

回复此楼

» 猜你喜欢

体制内长辈说体制内绝大部分一辈子在底层，如同你们一样大部分普通教师忙且收入低已经有12人回复
过年走亲戚时感受到了所开私家车的鄙视链已经有9人回复
今年春晚有几个节目很不错，点赞！已经有10人回复
情人节自我反思：在爱情中有过遗憾吗？已经有10人回复
基金正文30页指的是报告正文还是整个申请书已经有5人回复

1楼 2009-10-23 11:02:48

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

formleaf

木虫 (正式写手)

应助: 0 (幼儿园)
贵宾: 1.097
金币: 3383.1
散金: 2780
红花: 3
帖子: 991
在线: 69.6小时
虫号: 698652
注册: 2009-02-09
性别: GG
专业: 组合数学

续上面的内容

infinity, but extremely slowly. Nevertheless, this is the first explicitly quantitative version of the density Hales-Jewett theorem.

The argument is based on the density increment argument as pioneered by Roth, and also used in later papers of Ajtai-Szemerédi and Shkredov on the corners problem, which was also influential in our current work (though, perhaps paradoxically, the generality of our setting makes our argument simpler than the above arguments, in particular allowing one to avoid use of the Fourier transform, regularity lemma, or Szemerédi’s theorem). I discuss the argument in the first part of this previous blog post.

I’ll end this post with an open problem. In our paper, we cite the work of P. L. Varnavides, who was the first to observe the elementary averaging argument that showed that Roth’s theorem (which showed that dense sets of integers contained at least one progression of length three) could be amplified (to show that there was in some sense a “dense” set of arithmetic progressions of length three). However, despite much effort, we were not able to expand “P.” into the first name. As one final task of the Polymath1 project, perhaps some readers with skills in detective work could lend a hand in finding out what Varnavides’ first name was?