A De Bruijn-Erdős theorem for posets

Type: 
Lecture
Audience: 
Open to the Public
Thursday, December 4, 2014 - 2:15pm
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Date: 
Thursday, December 4, 2014 - 2:15pm
Venue: MTA Rényi Intézet, (nagyterem - big hall)
 
Joint work with P. Aboulker, G. Lagarde, D. Malec and C. Tompkins
Abstract: 
We prove that an analogue of De Bruijn-Erdős theorem holds for partially ordered sets. The extremal configurations are determined as well as a general lower bound on the number of lines as a function of the height of the poset. We will also discuss how the notion of lines in posets relates to the notion of lines in 3-uniform hypergraphs introduced by Chen and Chvátal and partially verify a conjecture of Beaudou, Bondy, Chen, Chiniforooshan, Chudnovsky, Chvatal, Fraiman and Zwols.