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2021 Iterating the RSK bijection
Maria Gillespie, Jacob Hocevar, Ananya Kulshrestha, Kosha Upadhyay
Involve 14(3): 475-494 (2021). DOI: 10.2140/involve.2021.14.475

Abstract

We investigate the dynamics of the well-known RSK bijection on permutations when iterated on various reading words of the recording tableau. In the setting of the ordinary (row) reading word, we show that there is exactly one fixed point per partition shape, and that it is always reached within two steps from any starting permutation.

We also consider the modified dynamical systems formed by iterating RSK on the column reading word and the reversed reading word of the recording tableau. We show that the column reading word gives similar dynamics to the row reading word. On the other hand, for the reversed reading word, we always reach either a 2 -cycle or fixed point after two steps. In fact, we reach a fixed point if and only if the shape of the initial tableau is self-conjugate.

Citation

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Maria Gillespie. Jacob Hocevar. Ananya Kulshrestha. Kosha Upadhyay. "Iterating the RSK bijection." Involve 14 (3) 475 - 494, 2021. https://doi.org/10.2140/involve.2021.14.475

Information

Received: 1 October 2020; Accepted: 26 February 2021; Published: 2021
First available in Project Euclid: 30 July 2021

Digital Object Identifier: 10.2140/involve.2021.14.475

Subjects:
Primary: 05A05
Secondary: 05E99

Keywords: dynamical systems , permutations , RSK correspondence , Young tableaux

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2021
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