Multicolor chain avoidance in the Boolean lattice

Given a collection of colored chain posets, we estimate the number of colored subsets of the Boolean lattice which avoid all chains in the collection. We do this by applying the hypergraph container lemma recursively, with different uniformities at each stage, using a balanced supersaturation result...

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Bibliographic Details
Published in:European journal of combinatorics 2020-06, Vol.87, p.103135, Article 103135
Main Authors: Spink, Hunter, Tiba, Marius
Format: Article
Language:English
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Summary:Given a collection of colored chain posets, we estimate the number of colored subsets of the Boolean lattice which avoid all chains in the collection. We do this by applying the hypergraph container lemma recursively, with different uniformities at each stage, using a balanced supersaturation result for a certain non-uniform hypergraph encoding forbidden configurations.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2020.103135