A comment on Intersecting families of permutations

Yuval Filmus

In a groundbreaking paper, Ellis, Friedgut and Pilpel showed that $t$-intersecting families of permutations contain at most $(n-t)!$ permutations, for large enough $n$. They also identified the extremal families: they are all $t$-cosets.

Unfortunately, Section 5 of the paper, which identifies the extremal families, is wrong. Fortunately, the identification follows from a different paper of Ellis, which is already mentioned in the original paper. A different proof follows from our work on complexity measures on the symmetric group.


 author = {Yuval Filmus},
 title = {A comment on Intersecting Families of Permutations},
 howpublished = {arXiv:1706.10146},
 year = {2017}
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