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arXiv · 2509.16355

The Sunflower-Free Process

Patrick Bennett·Amanda Priestley
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Abstract

An $r$-sunflower is a collection of $r$ sets such that the intersection of any two sets in the collection is identical. We analyze a random process which constructs a $w$-uniform $r$-sunflower free family starting with an empty family and at each step adding a set chosen uniformly at random from all choices that could be added without creating an $r$-sunflower with the previously chosen sets. To analyze this process, we extend results of the first author and Bohman arXiv:1308.3732v5 [math.CO], who analyzed a general random process which adds one object at a time chosen uniformly at random from all objects that can be added without creating certain forbidden subsets.

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Patrick Bennett, Amanda Priestley. 2025-09-19. The Sunflower-Free Process. https://arxiv.org/abs/2509.16355

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