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Fixes mis-aimed styling.

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Shoofle 2014-05-23 12:41:56 -04:00
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articles/tamari.article.html
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@ -6,7 +6,7 @@
<figcaption>A (trivial) Tamari lattice, generated by the associations of three elements. <a class="source" href="/tamari/tamari_3.dot">Source file.</a></figcaption>
</figure>
<p>Oh - oh dear. How'd that get there? Okay, that's not a very good example.</p>
<p>There are many ways to generate and think of <code>a</code> Tamari lattice. The way I prefer to think of it is this: Consider some binary operation - <code>a</code> way to use two things to make <code>a</code> new one. You want to combine <code>a</code> bunch. So long as you have three or more elements, there's more than one way to combine them - if you've got <code>a</code>, <code>b</code>, and <code>c</code>, you could combine <code>b</code> and <code>c</code>, and then combine the product of that with <code>a</code>, <em>or</em> you could combine <code>a</code> and <code>b</code>, and then combine that with <code>c</code>. We're going to pretend you can't combine <code>a</code> and <code>c</code> (although maybe that would produce more pictures...). The way we write combining two elements is like this: <code>(a, b)</code>. So that means that the first way of combing <code>a</code>, <code>b</code>, and <code>c</code> is written like so: <code>(a, (b, c))</code>. The second way would be <code>((a, b), c)</code>.</p>
<p>There are many ways to generate and think of a Tamari lattice. The way I prefer to think of it is this: Consider some binary operation - a way to use two things to make a new one. You want to combine a bunch. So long as you have three or more elements, there's more than one way to combine them - if you've got <code>a</code>, <code>b</code>, and <code>c</code>, you could combine <code>b</code> and <code>c</code>, and then combine the product of that with <code>a</code>, <em>or</em> you could combine <code>a</code> and <code>b</code>, and then combine that with <code>c</code>. We're going to pretend you can't combine <code>a</code> and <code>c</code> (although maybe that would produce more pictures...). The way we write combining two elements is like this: <code>(a, b)</code>. So that means that the first way of combing <code>a</code>, <code>b</code>, and <code>c</code> is written like so: <code>(a, (b, c))</code>. The second way would be <code>((a, b), c)</code>.</p>
<p>Okay, got it? Good.</p>
<p>The game we play is this: You're allowed to step from one way of combining the elements to another, but only by <i class="keyword">left-association</i>: turning <code>(a, (b, c))</code> into <code>((a, b), c)</code>.</p>
<p>The only other rule is that if you can step from one combination to another, the second one has to be drawn below the first one when you list them all out.</p>