The Proportion of Permutations Fixing a k-Set
An asymptotic formula for $p(k)$, the limiting probability that a random permutation has an invariant set of size $k$: it is asymptotically $k^{-\delta}(1+o(1))$ times a smooth positive function, sharpening a line of estimates running through Łuczak-Pyber and Eberhard-Ford-Green.
Exact FrontierDelta
Scope and record
Occurred: Apr 30, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: The Proportion of Permutations Fixing a k-Set · Permutations fixing a k-set
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Ben Green
human · human collaborator
Mehtaab Sawhney
human · human collaborator
GPT o4-mini
model · ai model contributor · OpenAI
ChatGPT Pro 5.4
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Mehtaab Sawhney
This event attributed to Ben Green
This event attributed to ChatGPT Pro 5.4
This event attributed to GPT o4-mini