Abstract
In [19], a $$q$$ 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 $$q$$ q -weighted versions of the Robinson---Schensted algorithm which have recently been introduced by Borodin---Petrov [2].
Highlights
In [19], a q-weighted version of the Robinson–Schensted (RS) algorithm was introduced
The proof uses a generalisation of the growth diagram approach introduced by [5,6,7,8]
We describe it in a way that suits the growth diagram
Summary
In [19], a q-weighted version of the Robinson–Schensted (RS) algorithm was introduced. J Algebr Comb (2014) 40:743–770 have recently introduced a q-weighted version of the row insertion algorithm, which is defined to the column insertion version of [19]; they consider a wider family of such algorithms (and, more generally, dynamics on Gelfand–Tsetlin patterns), some of which fall into the framework considered in the present paper, and can be shown to have the symmetry property Knuth [13] generalised the usual row insertion algorithm to one which takes matrix input, which we refer to as Robinson–Schensted–Knuth (RSK) algorithm For this algorithm, the symmetry property is that the output tableau pair is interchanged if the matrix is transposed. The special structure of growth diagram can be extended to a class of algorithms what we will call branching algorithms, which include the q-weighted column and row insertion algorithms It is this approach which we use in this paper.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
