Frankl's diversity theorem for permutations
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910020170416128 |
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| author | Inozemtsev, Eduard Kupavskii, Andrey |
| author_facet | Inozemtsev, Eduard Kupavskii, Andrey |
| contents | In 1987, Frankl proved an influential stability result for the Erd\H os--Ko--Rado theorem, which bounds the size of an intersecting family in terms of its distance from the nearest (subset of) star or trivial intersecting family. It is a far-reaching extension of the Hilton--Milner theorem. In this paper, we prove its analogue for permutations on $\{1,\ldots, n\}$, provided $n$ is large. This provides a similar extension of a Hilton--Milner type result for permutations proved by Ellis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_11796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Frankl's diversity theorem for permutations Inozemtsev, Eduard Kupavskii, Andrey Combinatorics Discrete Mathematics In 1987, Frankl proved an influential stability result for the Erd\H os--Ko--Rado theorem, which bounds the size of an intersecting family in terms of its distance from the nearest (subset of) star or trivial intersecting family. It is a far-reaching extension of the Hilton--Milner theorem. In this paper, we prove its analogue for permutations on $\{1,\ldots, n\}$, provided $n$ is large. This provides a similar extension of a Hilton--Milner type result for permutations proved by Ellis. |
| title | Frankl's diversity theorem for permutations |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2602.11796 |