@article{f730f02ad7d949bc9626209c1520651c,
title = "Saturating Sperner Families",
abstract = "A family F ⊆ 2[n] saturates the monotone decreasing property P if F satisfies P and one cannot add any set to F such that property P is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets.",
keywords = "Extremal set theory, Saturation, Sperner property",
author = "D{\'a}niel Gerbner and Bal{\'a}zs Keszegh and Nathan Lemons and Cory Palmer and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi and Bal{\'a}zs Patk{\'o}s",
note = "Funding Information: The research of B. Patk{\'o}s{\textquoteright}s was supported by Hungarian National Scientific Fund, Grant Numbers: OTKA K-69062 and PD-83586. Funding Information: The research of D. Gerbner, B. Keszegh and C. Palmer was supported by Hungarian National Scientific Fund, Grant number: OTKA NK-78439. Funding Information: The European Union and the European Social Fund have provided financial support to the project under the Grant Agreement No. T{\'A}MOP 4.2.1./B-09/1/KMR-2010-0003 to D. P{\'a}lv{\"o}lgyi. ",
year = "2013",
month = sep,
doi = "10.1007/s00373-012-1195-6",
language = "English",
volume = "29",
pages = "1355--1364",
journal = "Graphs and Combinatorics",
issn = "0911-0119",
publisher = "Springer Japan",
number = "5",
}