@article{cab194244073480c8cb48bd525794e4d,
title = "Structure and supersaturation for intersecting families",
abstract = "The extremal problems regarding the maximum possible size of intersecting families of various combinatorial objects have been extensively studied. In this paper, we investigate supersaturation extensions, which in this context ask for the minimum number of disjoint pairs that must appear in families larger than the extremal threshold. We study the minimum number of disjoint pairs in families of permutations and in k-uniform set families, and determine the structure of the optimal.",
author = "J{\'o}zsef Balogh and Hong Liu and Maryam Sharifzadeh and Shagnik Das and Tuan Tran",
note = "Partially supported by NSF Grant DMS-1500121 and by the Langan Scholar Fund (UIUC). Supported by GIF grant G-1347-304.6/2016. Supported by the Leverhulme Trust Early Career Fellowship ECF-2016-523. Supported by ERC grant 306493 and the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Curie grant agreement No 752426. Supported by the Alexander Humboldt Foundation, and by the GACR grant GJ16-07822Y, with institutional support RVO:67985807. ∗Partially supported by NSF Grant DMS-1500121 and by the Langan Scholar Fund (UIUC). †Supported by GIF grant G-1347-304.6/2016. ‡Supported by the Leverhulme Trust Early Career Fellowship ECF-2016-523. §Supported by ERC grant 306493 and the European Union{\textquoteright}s Horizon 2020 research and innovation programme under the Marie Curie grant agreement No 752426. ¶Supported by the Alexander Humboldt Foundation, and by the GACR grant GJ16-07822Y, with institutional support RVO:67985807.",
year = "2019",
doi = "10.37236/7683",
language = "English (US)",
volume = "26",
journal = "Electronic Journal of Combinatorics",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "2",
}