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Supersaturation in posets and applications involving the container method

Abstract:

We consider ‘supersaturation’ problems in partially ordered sets (posets) of the following form. Given a finite poset P and an integer m greater than the cardinality of the largest antichain in P, what is the minimum number of comparable pairs in a subset of P of cardinality m? We provide a framework for obtaining lower bounds on this quantity based on counting comparable pairs relative to a random chain and apply this framework to obtain supersaturation results for three classical posets: th...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Accepted Manuscript

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Publisher copy:
10.1016/j.jcta.2017.08.019

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
Merton College
Sudakov, B More by this author
Publisher:
Elsevier Publisher's website
Journal:
Journal of Combinatorial Theory, Series A Journal website
Volume:
154
Pages:
247-284
Publication date:
2017-09-14
DOI:
ISSN:
0097-3165
Pubs id:
pubs:734439
URN:
uri:e7b8d4e1-8dda-419b-afe2-665ac78dda3a
UUID:
uuid:e7b8d4e1-8dda-419b-afe2-665ac78dda3a
Local pid:
pubs:734439

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