Fixed Point Homing Shuffles

2024/10/29 by Jonathan Parlett, Parlett, Jonathan
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2410.22548

openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a family of maps from S_n → 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.

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