<div class="thumb tright"><div class="thumbinner" style="width:152px;"><a href="//commons.wikimedia.org/wiki/File:Cube_Hasse_diagram.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Cube_Hasse_diagram.svg/150px-Cube_Hasse_diagram.svg.png" decoding="async" width="150" height="196" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Cube_Hasse_diagram.svg/225px-Cube_Hasse_diagram.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/c/c8/Cube_Hasse_diagram.svg/300px-Cube_Hasse_diagram.svg.png 2x" data-file-width="1307" data-file-height="1712"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Cube_Hasse_diagram.svg" class="internal" title="Enlarge"></a></div>Cube</div></div></div>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><a href="//commons.wikimedia.org/wiki/File:Weak_orderings_3.svg" class="image"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Weak_orderings_3.svg/220px-Weak_orderings_3.svg.png" decoding="async" width="220" height="193" class="thumbimage" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Weak_orderings_3.svg/330px-Weak_orderings_3.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Weak_orderings_3.svg/440px-Weak_orderings_3.svg.png 2x" data-file-width="773" data-file-height="678"></a>  <div class="thumbcaption"><div class="magnify"><a href="//commons.wikimedia.org/wiki/File:Weak_orderings_3.svg" class="internal" title="Enlarge"></a></div>The 13 ordered set partitions</div></div></div>
<p>Implications between the <span style="white-space:nowrap"><a href="https://en.wikipedia.org/wiki/On-Line_Encyclopedia_of_Integer_Sequences" title="Sloane's"><img alt="Sloane's" src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/11px-OEISicon_light.svg.png" decoding="async" width="11" height="15" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/17px-OEISicon_light.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/d/d8/OEISicon_light.svg/22px-OEISicon_light.svg.png 2x" data-file-width="409" data-file-height="556"></a> <a href="//oeis.org/A000629" class="extiw" title="oeis:A000629">A000629</a></span>(3) = 26 statements with 3 variables in <a href="https://en.wikipedia.org/wiki/first-order_logic" class="extiw" title="w:first-order logic">first-order logic</a>
</p><p>The formulas are represented by <a href="https://en.wikipedia.org/wiki/Weak_ordering" class="extiw" title="w:Weak ordering">ordered set partitions</a>. Black stands for the universal <a href="https://en.wikipedia.org/wiki/Quantification" class="extiw" title="w:Quantification">quantifier</a>, red for the existential one.
</p><p>The basic structure of this Graph is like the cube shown on the right.
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