RSK via local transformations

TL;DR

This paper presents a novel way to understand the RSK correspondence using local transformations called toggles, providing a new perspective on this classical combinatorial algorithm.

Contribution

It introduces a local transformation framework for the RSK correspondence, offering a new conceptual approach based on toggles.

Findings

Defines RSK via local toggle transformations

Provides a new combinatorial perspective on RSK

Circulates as an unpublished note since 2014

Abstract

We explain how to define the Robinson-Schensted-Knuth (RSK) correspondence in terms of local transformations called "toggles." (This note, which is not intended for publication and which is based on presentations of Alex Postnikov, was written in 2014 and has been circulating since then. We are finally posting it to the arXiv for preservation purposes.)