Fixed Point Homing Shuffles
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909742312456192 |
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| author | Parlett, Jonathan |
| author_facet | Parlett, Jonathan |
| contents | We study a family of maps from $S_n \to S_n$ we call fixed point homing shuffles. These maps generalize a few known problems such as Conway's Topswops, and a card shuffling process studied by Gweneth McKinley. We show that the iterates of these homing shuffles always converge, and characterize the set $U_n$ of permutations that no homing shuffle sorts. We also study a homing shuffle that sorts anything not in $U_n$, and find how many iterations it takes to converge in the worst case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fixed Point Homing Shuffles Parlett, Jonathan Combinatorics We study a family of maps from $S_n \to S_n$ we call fixed point homing shuffles. These maps generalize a few known problems such as Conway's Topswops, and a card shuffling process studied by Gweneth McKinley. We show that the iterates of these homing shuffles always converge, and characterize the set $U_n$ of permutations that no homing shuffle sorts. We also study a homing shuffle that sorts anything not in $U_n$, and find how many iterations it takes to converge in the worst case. |
| title | Fixed Point Homing Shuffles |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2410.22548 |