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        <title>Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms</title>
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                <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>

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