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

Abstract

In [19], a q-weighted version of the Robinson–Schensted algorithm was introduced. In this paper, we show that this algorithm has a symmetry property analogous to the well-known symmetry property of the usual Robinson–Schensted algorithm. The proof uses a generalisation of the growth diagram approach introduced by Fomin [5–8]. This approach, which uses ‘growth graphs’, can also be applied to a wider class of insertion algorithms which have a branching structure, including some of the other q-weighted versions of the Robinson–Schensted algorithm which have recently been introduced by Borodin–Petrov [2].