# Induced and non-induced poset saturation problems

@article{Keszegh2021InducedAN,
title={Induced and non-induced poset saturation problems},
author={Bal{\'a}zs Keszegh and Nathan Lemons and Ryan R. Martin and D{\"o}m{\"o}t{\"o}r P{\'a}lv{\"o}lgyi and Bal{\'a}zs Patk{\'o}s},
journal={J. Comb. Theory, Ser. A},
year={2021},
volume={184},
pages={105497}
}
• Published 9 March 2020
• Mathematics
• J. Comb. Theory, Ser. A

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Saturating Sperner Families
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Graphs Comb.
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Electron. J. Comb.
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This work asymptotically determines the size of the largest family F of subsets of subset of $\{1,\dots,n\}$ not containing a given poset P if the Hasse diagram of $P$ is a tree.
Progress on poset-free families of subsets
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Increasing attention is being paid to the study of families of subsets of an n-set that contain no subposet P. Especially, we are interested in such families of maximum size given P and n. For
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A new approach is used to apply methods from extremal graph theory and probability theory to identify new classes of posets H, for which La(n, H) can be determined asymptotically as n → ∞ for various poset H, including two-end-forks, up-down trees, and cycles C4k on two levels.
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