Every Poset Has a Central Element

@article{Linial1985EveryPH,
  title={Every Poset Has a Central Element},
  author={Nathan Linial and Michael E. Saks},
  journal={J. Comb. Theory, Ser. A},
  year={1985},
  volume={40},
  pages={195-210}
}
It is proved that there exists a constant 6, f > 6 > 0, such that in every finite partially ordered set there is an element such that the fraction of order ideals containing that element is between 6 and 1-6. It is shown that 6 can be taken to be at least (3-log, 5)/4~0.17. This settles a question asked independently by Colburn and Rival, and Rosenthal. The… CONTINUE READING