Department of Mathematics

Combinatorics and Graph Theory

  •  Progress on the 1/3-2/3 Conjecture
  •  04/11/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Emily Olson, MSU

In a partially ordered set P, let a pair of elements (x,y) be called alpha-balanced if the proportion of linear extensions that has x before y is between alpha and 1-alpha. The 1/3-2/3 Conjecture states that every finite poset which is not a chain has some 1/3-balanced pair. While the conjecture remains unsolved, we extend the list of posets that satisfy the conjecture by adding certain lattices, including products of two chains, as well as posets that correspond to Young diagrams.

 

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Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science