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        <description>Oriented swap process and last passage percolation notes

This page can be used for writing up results in more or less finished form. See the talk page for discussion and more sketchy/incomplete ideas.

1 Definitions

	*  Oriented swap process (OSP)
	*  Last passage percolation (LPP)\begin{align*}
T(a,b;c,d) &amp;= \max_{\pi \in \Pi_{(a,b)\to(c,d)}} \sum_{(i,j)\in \pi} X_{i,j} \quad \textrm{(last passage percolation time from }(a,b)\textrm{ to }(c,d) 
\textrm{)}
\\
\mathbf{V}^n &amp;= (V^n_1,\ldots,V^n_…</description>
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Section 1

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum</description>
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placeholder page for notes about sphere packing and related topics -- add content</description>
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        <description>Dan Romik's page

Mathematician at UC Davis. Interested in combinatorics, number theory, probability and more. Currently busy building and improving this site, among other things.

You can learn about my research at my personal web page. (I may eventually move some of that material to this space.)</description>
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