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Diffstat (limited to 'posts/2014-04-01-q-robinson-schensted-symmetry-paper.org')
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diff --git a/posts/2014-04-01-q-robinson-schensted-symmetry-paper.org b/posts/2014-04-01-q-robinson-schensted-symmetry-paper.org new file mode 100644 index 0000000..b1c967d --- /dev/null +++ b/posts/2014-04-01-q-robinson-schensted-symmetry-paper.org @@ -0,0 +1,16 @@ +#+title: Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms +#+date: <2014-04-01> + +In [[http://link.springer.com/article/10.1007/s10801-014-0505-x][this +paper]] 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. + +#+caption: Growth graph of q-RS for 1423 +[[../assets/resources/1423graph.jpg]] + +Above is the growth graph of the \(q\)-weighted Robinson-Schensted +algorithm for the permutation \({1 2 3 4\choose1 4 2 3}\). |