Saved in:
| Main Authors: | , , , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.24255 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910250734452736 |
|---|---|
| author | Herden, Daniel Hunziker, Markus Meddaugh, Jonathan Sepanski, Mark R. Engelthaler, Lauren Feigert, Jonathan Gulding, Teresa Hernández-Rodríguez, Jesús Minyard, Mitchell Rosengartner, Kyle Saparamadu, Dona Ishara N. Stansbury, Robert |
| author_facet | Herden, Daniel Hunziker, Markus Meddaugh, Jonathan Sepanski, Mark R. Engelthaler, Lauren Feigert, Jonathan Gulding, Teresa Hernández-Rodríguez, Jesús Minyard, Mitchell Rosengartner, Kyle Saparamadu, Dona Ishara N. Stansbury, Robert |
| contents | Young tableaux are fundamental objects in algebraic combinatorics and representation theory, with operations such as promotion and jeu de taquin playing a central role in their structure and applications. While these operations are well understood for finite tableaux, their behavior on infinite tableaux has so far been studied mainly within probabilistic frameworks. In this paper, we investigate jeu de taquin on infinite standard Young tableaux from a purely combinatorial and dynamical point of view. We analyze the action of jeu de taquin on infinite shapes, describe the structure of inverse images, and classify tableaux exhibiting periodic, pre-periodic, and recurrent behavior. We also introduce a natural metric on the space of infinite tableaux and show that jeu de taquin defines a chaotic dynamical system in the sense of Devaney. These results extend classical tableau theory to infinite settings and identify connections between combinatorial dynamics and infinite representation-theoretic structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24255 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Herden, Daniel Hunziker, Markus Meddaugh, Jonathan Sepanski, Mark R. Engelthaler, Lauren Feigert, Jonathan Gulding, Teresa Hernández-Rodríguez, Jesús Minyard, Mitchell Rosengartner, Kyle Saparamadu, Dona Ishara N. Stansbury, Robert Combinatorics Primary: 05E10, Secondary: 20B30 Young tableaux are fundamental objects in algebraic combinatorics and representation theory, with operations such as promotion and jeu de taquin playing a central role in their structure and applications. While these operations are well understood for finite tableaux, their behavior on infinite tableaux has so far been studied mainly within probabilistic frameworks. In this paper, we investigate jeu de taquin on infinite standard Young tableaux from a purely combinatorial and dynamical point of view. We analyze the action of jeu de taquin on infinite shapes, describe the structure of inverse images, and classify tableaux exhibiting periodic, pre-periodic, and recurrent behavior. We also introduce a natural metric on the space of infinite tableaux and show that jeu de taquin defines a chaotic dynamical system in the sense of Devaney. These results extend classical tableau theory to infinite settings and identify connections between combinatorial dynamics and infinite representation-theoretic structures. |
| title | Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux |
| topic | Combinatorics Primary: 05E10, Secondary: 20B30 |
| url | https://arxiv.org/abs/2605.24255 |