The role of paths in Robinson–Schensted algorithm (RS), and Kerov, Kirillov and Reshetikhin bijection (KKR)

In this work we want to amplify the RS algorithm in the language of paths. Thus, it is a continuation of the previous work [Lulek et al., to appear in Mol. Phys.], where the magnetic interpretation of RS algorithm was given. We also want to present the intermediative role of paths in bijection between standard Young tableaux and rigged configurations. We will treat the paths as a bridge which allow us to move between this two objects.