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In O'Connell-Pei(2013) a q-weighted version of the Robinson-Schenstedalgorithm was introduced. In this paper we show that this algorithm has asymmetry property analogous to the well known symmetry property of the normalRobinson-Schensted algorithm. The proof uses a generalisation of the growthdiagram approach introduced by Fomin(1979,1986,1994,1995). This approach, whichuses "growth graphs", can also be applied to a wider class of insertionalgorithms which have a branching structure, including some of the otherq-weighted versions of the Robinson-Schensted algorithm which have recentlybeen introduced by Borodin-Petrov(2013).

A symmetry property for q-weighted Robinson-Schensted algorithms and other branching insertion algorithms