Fixed Point Homing Shuffles
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...
Uloženo v:
| Vydáno v: | Discrete mathematics and theoretical computer science Ročník 27:1, Permutation...; číslo Special issues |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Discrete Mathematics & Theoretical Computer Science
18.08.2025
|
| Témata: | |
| ISSN: | 1365-8050, 1365-8050 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Shrnutí: | 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.
Updated formatting to fit with DMTCS requirements |
|---|---|
| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.46298/dmtcs.14653 |