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research
Intersecting P-free families
Authors
Dániel Gerbner
Abhishek Methuku
Casey Tompkins
Publication date
1 January 2017
Publisher
'Elsevier BV'
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arXiv
Abstract
We study the problem of determining the size of the largest intersecting P-free family for a given partially ordered set (poset) P. In particular, we find the exact size of the largest intersecting B-free family where B is the butterfly poset and classify the cases of equality. The proof uses a new generalization of the partition method of Griggs, Li and Lu. We also prove generalizations of two well-known inequalities of Bollobás and Greene, Katona and Kleitman in this case. Furthermore, we obtain a general bound on the size of the largest intersecting P-free family, which is sharp for an infinite class of posets originally considered by Burcsi and Nagy, when n is odd. Finally, we give a new proof of the bound on the maximum size of an intersecting k-Sperner family and determine the cases of equality. © 2017 Elsevier Inc
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oai:real.mtak.hu:65650
Last time updated on 21/11/2017