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arXiv · 2310.11662

Note on down-set thresholds

Lutz Warnke
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Abstract

Gunby-He-Narayanan showed that the logarithmic gap predictions of Kahn-Kalai and Talagrand (proved by Park-Pham and Frankston-Kahn-Narayanan-Park) about thresholds of up-sets do not apply to down-sets. In particular, for the down-set of triangle-free graphs, they showed that there is a polynomial gap between the threshold and the factional expectation threshold. In this short note we give a simpler proof of this result, and extend the polynomial threshold gap to down-sets of F-free graphs.

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Lutz Warnke. 2023-10-18. Note on down-set thresholds. https://doi.org/10.1002/rsa.21194

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