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----
-template: oldpost
-title: Symmetry property of \(q\)-weighted Robinson-Schensted algorithms and branching algorithms
-date: 2014-04-01
-comments: true
-archive: false
-tags: RS, growth_diagrams
----
-In [this paper](http://link.springer.com/article/10.1007/s10801-014-0505-x) 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.
-
-![Growth graph of q-RS for 1423](../assets/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}\\).