Matchings in permutations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909017781043200 |
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| author | Inozemtsev, Eduard Kolupaev, Dmitrii Kupavskii, Andrey |
| author_facet | Inozemtsev, Eduard Kolupaev, Dmitrii Kupavskii, Andrey |
| contents | We say that two permutations $[n]\to [n]$ intersect if they map some element $x$ to the same element $y$. A matching in a family of permutations is a collection of pairwise disjoint permutations. In this paper, we study families of permutations with no matchings of size $s$. In particular, we obtain a characterization of the largest $s$-matching-free families and a Hilton--Milner type result. We also obtain results for the families of derangements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Matchings in permutations Inozemtsev, Eduard Kolupaev, Dmitrii Kupavskii, Andrey Combinatorics Discrete Mathematics We say that two permutations $[n]\to [n]$ intersect if they map some element $x$ to the same element $y$. A matching in a family of permutations is a collection of pairwise disjoint permutations. In this paper, we study families of permutations with no matchings of size $s$. In particular, we obtain a characterization of the largest $s$-matching-free families and a Hilton--Milner type result. We also obtain results for the families of derangements. |
| title | Matchings in permutations |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2605.04987 |