Investigations in Topdrops
ISEF · 2021 Mathematics Third Award
Overview
Topdrops, a mapping of permutations first introduced by John Horton Conway, is examined. Topdrops has so far been under-researched compared to the similar topswops variant. A proof that the topdrops mapping is bijective is provided. Various orbits are produced when the mapping is applied repeatedly. Three proofs about the numbers of orbits of small sizes are stated. Observational data on the numbers of orbits of larger sizes are also provided. In addition, several observations are provided that suggest further avenues of research for this largely unexplored problem.
Awards (2)
- Third Award of $1,000 $1,000
- American Mathematical Society: Certificate of Honorable Mention
Competition history
- ISEF 2021
Resources
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