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Iterating the
RSK bijection
Maria Gillespie, Jacob Hocevar, Ananya Kulshrestha and Kosha Upadhyay
Vol. 14 (2021), No. 3, 475–494
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Abstract |
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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 -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. |
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Keywords
Young tableaux, permutations, dynamical systems, RSK
correspondence
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Mathematical Subject Classification
Primary: 05A05
Secondary: 05E99
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Milestones
Received: 1 October 2020
Revised: 11 February 2021
Accepted: 26 February 2021
Published: 17 July 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Maria Gillespie | |
| Department of Mathematics Colorado State University Fort Collins, CO United States |
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| Jacob Hocevar | |
| McKinney Christian Academy Plano, TX United States |
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| Ananya Kulshrestha | |
| Irvington High School Fremont, CA United States |
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| Kosha Upadhyay | |
| Bellevue High School Bellevue, WA United States |
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