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<?xml version="1.0"?>
<api>
  <query-continue>
    <search sroffset="10" />
  </query-continue>
  <query>
    <search>
      <p ns="0" title="Complexity of a set" snippet="...3]^n&amp;lt;/math&amp;gt; by taking the set of all sequences x such that the 1-set of x (&lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; the set of coordinates i where &amp;lt;math&amp;gt;x_i=1&amp;lt;/math&amp;gt;) belongs to &amp;lt;math&amp;gt;\mathca&#10;" size="3043" wordcount="553" timestamp="2013-10-30T20:06:14Z" />
      <p ns="0" title="A second Fourier decomposition related to Sperner&#039;s theorem" snippet=".... And since the expectation of &amp;lt;math&amp;gt;w_{i,p}(x)^2&amp;lt;/math&amp;gt; is 1 (this is the &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; of the condition &amp;lt;math&amp;gt;(1-p)a_p^2+pb_p^2=1&amp;lt;/math&amp;gt;), the entire expectation &#10;" size="12585" wordcount="2517" timestamp="2009-02-27T21:37:26Z" />
      <p ns="0" title="A second outline of a density-increment argument" snippet="...h&amp;gt;\mathcal{U}&amp;lt;/math&amp;gt; be a dense collection of subsets of &amp;lt;math&amp;gt;[n],&amp;lt;/math&amp;gt; &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that the 1-set &amp;lt;math&amp;gt;\mathcal{U}\otimes[2]^n&amp;lt;/math&amp;gt; has density &amp;lt;math&amp;gt;\thet&#10;" size="16130" wordcount="2888" timestamp="2009-03-18T12:59:03Z" />
      <p ns="0" title="Proof of DHJ(3) via density-increment" snippet="...at any string drawn from the Pólya Urn distribution is [[nondegenerate]], &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; it contains at least one of each character in &amp;lt;math&amp;gt;[3]&amp;lt;/math&amp;gt;.&#10;" size="14554" wordcount="2401" timestamp="2009-03-20T21:58:03Z" />
      <p ns="0" title="Kakeya problem" snippet="...&amp;gt;k_4\le 27&amp;lt;/math&amp;gt;. Indeed, it seems likely that &amp;lt;math&amp;gt;k_4=27&amp;lt;/math&amp;gt; holds, &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that in &amp;lt;math&amp;gt;{\mathbb F}_3^4&amp;lt;/math&amp;gt; one cannot get away with just &amp;lt;math&amp;gt;26&#10;" size="4701" wordcount="851" timestamp="2009-06-05T07:35:31Z" />
      <p ns="0" title="Insensitive.tex" snippet="...late for this subspace as $\sigma \in ([k-1] \cup \{k+1, \dots, k+d\})^J$, &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that $\chg{\sigma}{(k+t)}{\ell} \in A_{x_\barJ}$ for each $t \in [d]$ and $&#10;" size="7629" wordcount="1322" timestamp="2009-06-11T20:05:54Z" />
      <p ns="0" title="Easy.tex" snippet="...late for this subspace as $\sigma \in ([k-1] \cup \{k+1, \dots, k+d\})^J$, &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that $\chg{\sigma}{(k+t)}{\ell} \in B_{x_\barJ}$ for each $t \in [d]$ and $&#10;" size="9055" wordcount="1548" timestamp="2009-06-25T04:22:23Z" />
      <p ns="0" title="Concepts.tex" snippet="...his distribution is very ``far&#039;&#039; from the uniform distribution on $[3]^n$, &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that even if $\unif_3^{\ot n}(A) \geq \delta$, the probability that $\chg{\&#10;" size="15593" wordcount="2498" timestamp="2009-07-08T20:24:24Z" />
      <p ns="0" title="The Erdős discrepancy problem" snippet="...ative function f from &amp;lt;math&amp;gt;\mathbb{N}&amp;lt;/math&amp;gt; to a finite Abelian group G (&lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; that f(mn)=f(m)+f(n) for every m,n) and a function h from G to {-1,1} such &#10;" size="29508" wordcount="4312" timestamp="2015-09-21T17:31:38Z" />
      <p ns="0" title="Generalize to a graph-theoretic formulation" snippet="Here is a possible &lt;span class=&#039;searchmatch&#039;&gt;meaning&lt;/span&gt; for “completely multiplicative”, although it is extremely messy and cou&#10;" size="4137" wordcount="763" timestamp="2010-05-25T16:39:20Z" />
    </search>
  </query>
</api>