Year: 2025
Type: article
Abstract: 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
DOI: 10.46298/dmtcs.14653
Author: Jonathan Parlett
Institution: Drexel University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Funder: Drexel University
OpenAlex ID: W4413284107