site/posts/2014-04-01-q-robinson-schensted-symmetry-paper.html


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

<!doctype html>
<html lang="en">
    <head>
        <meta charset="utf-8">
        <title>Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms</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>
    </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> Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms </h2>
                <p>Posted on 2014-04-01</p>
                    <p>In <a href="http://link.springer.com/article/10.1007/s10801-014-0505-x">this paper</a> a symmetry property analogous to the well known symmetry property of the normal Robinson-Schensted algorithm has been shown for the \(q\)-weighted Robinson-Schensted algorithm. The proof uses a generalisation of the growth diagram approach introduced by Fomin. This approach, which uses “growth graphs”, can also be applied to a wider class of insertion algorithms which have a branching structure.</p>
<figure>
<img src="../assets/resources/1423graph.jpg" alt="Growth graph of q-RS for 1423" /><figcaption>Growth graph of q-RS for 1423</figcaption>
</figure>
<p>Above is the growth graph of the \(q\)-weighted Robinson-Schensted algorithm for the permutation \({1 2 3 4\choose1 4 2 3}\).</p>

            </div>
        </div>
    </body>
</html>