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...

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Vydáno v:Discrete mathematics and theoretical computer science Ročník 27:1, Permutation...; číslo Special issues
Hlavní autor: Parlett, Jonathan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Discrete Mathematics & Theoretical Computer Science 18.08.2025
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ISSN:1365-8050, 1365-8050
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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