Abstract:A set of permutations of $\{1,2,\dots,n\}$ is $t$-intersecting if any two permutations agree on at least $t$ inputs. A recent work by Kupavskii, in the spirit of the Erdős-Ko-Rado Theorem, shows that for all $t\leq n-O\left(\frac{n\log\log n}{\log n}\right)$, every $t$-intersecting family of permutations of $\{1,2,\dots,n\}$ with the maximum size must be isomorphic to the set $$A_k = \{\sigma : \sigma(i)=i\text{ for at least } t+k \text{ indices } i\in\{1,2,\dots,t+2k\}\}$$ for some $k$. By refining Kupavskii's spread approximation technique, we prove that this conclusion holds for a wider range of $t\leq n-n^{5/7+\varepsilon}$.
| Comments: | 31 pages |
| Subjects: | Combinatorics (math.CO) |
| MSC classes: | 05D05 |
| Cite as: | arXiv:2605.26051 [math.CO] |
| (or arXiv:2605.26051v1 [math.CO] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26051 arXiv-issued DOI via DataCite (pending registration) |
From: Pitchayut Saengrungkongka [view email]
[v1]
Mon, 25 May 2026 17:12:19 UTC (55 KB)
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