The Proportion of Permutations Fixing a k-Set
Statement
An asymptotic formula for , the limiting probability that a random permutation has an invariant set of size : it is asymptotically times a smooth positive function, sharpening a line of estimates running through Łuczak-Pyber and Eberhard-Ford-Green.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Ben Green and Mehtaab Sawhney, using GPT o4-mini, ChatGPT Pro 5.4That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The authors "originally discovered that g was almost constant via the use of GPT o4-mini. Upon being asked to prove this fact, the model suggested the broad strategy" (initially miscomputing an integral, then completing the evaluation after being pointed at Mellin transforms). A separate argument in the paper is ChatGPT Pro 5.4's, shortened and checked by the authors, kept because it was cleaner than their own.
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