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diff --git a/site-from-md/posts/2013-06-01-q-robinson-schensted-paper.html b/site-from-md/posts/2013-06-01-q-robinson-schensted-paper.html deleted file mode 100644 index 2ccaf87..0000000 --- a/site-from-md/posts/2013-06-01-q-robinson-schensted-paper.html +++ /dev/null @@ -1,52 +0,0 @@ -<!doctype html> -<html lang="en"> - <head> - <meta charset="utf-8"> - <title>A \(q\)-weighted Robinson-Schensted algorithm</title> - <link rel="stylesheet" href="../assets/css/default.css" /> - <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script> - <script src="../assets/js/analytics.js" type="text/javascript"></script> - </head> - <body> - <header> - <span class="logo"> - <a href="../blog.html">Yuchen's Blog</a> - </span> - <nav> - <a href="../index.html">About</a><a href="../postlist.html">All posts</a><a href="../blog-feed.xml">Feed</a> - </nav> - </header> - - <div class="main"> - <div class="bodyitem"> - <h2> A \(q\)-weighted Robinson-Schensted algorithm </h2> - <p>Posted on 2013-06-01</p> - <!DOCTYPE html> -<html xmlns="http://www.w3.org/1999/xhtml" lang="" xml:lang=""> -<head> - <meta charset="utf-8" /> - <meta name="generator" content="pandoc" /> - <meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes" /> - <title>Untitled</title> - <style> - code{white-space: pre-wrap;} - span.smallcaps{font-variant: small-caps;} - span.underline{text-decoration: underline;} - div.column{display: inline-block; vertical-align: top; width: 50%;} - </style> - <!--[if lt IE 9]> - <script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv-printshiv.min.js"></script> - <![endif]--> -</head> -<body> -<p>In <a href="https://projecteuclid.org/euclid.ejp/1465064320">this paper</a> with <a href="http://www.bristol.ac.uk/maths/people/neil-m-oconnell/">Neil</a> we construct a \(q\)-version of the Robinson-Schensted algorithm with column insertion. Like the <a href="http://en.wikipedia.org/wiki/Robinson–Schensted_correspondence">usual RS correspondence</a> with column insertion, this algorithm could take words as input. Unlike the usual RS algorithm, the output is a set of weighted pairs of semistandard and standard Young tableaux \((P,Q)\) with the same shape. The weights are rational functions of indeterminant \(q\).</p> -<p>If \(q\in[0,1]\), the algorithm can be considered as a randomised RS algorithm, with 0 and 1 being two interesting cases. When \(q\to0\), it is reduced to the latter usual RS algorithm; while when \(q\to1\) with proper scaling it should scale to directed random polymer model in <a href="http://arxiv.org/abs/0910.0069">(O’Connell 2012)</a>. When the input word \(w\) is a random walk:</p> -<p>\begin{align*}\mathbb P(w=v)=\prod_{i=1}^na_{v_i},\qquad\sum_ja_j=1\end{align*}</p> -<p>the shape of output evolves as a Markov chain with kernel related to \(q\)-Whittaker functions, which are Macdonald functions when \(t=0\) with a factor.</p> -</body> -</html> - - </div> - </div> - </body> -</html> |