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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.16355 |
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| _version_ | 1866912595258114048 |
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| author | Bennett, Patrick Priestley, Amanda |
| author_facet | Bennett, Patrick Priestley, Amanda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16355 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Sunflower-Free Process Bennett, Patrick Priestley, Amanda Combinatorics Probability 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. |
| title | The Sunflower-Free Process |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2509.16355 |