- Sorting Probability for Linear Extensions
- Project Year:
2023
- REU Student (s):
Molly MacDonald | University of Notre Dame IN
- Student 1 Institution:
University of Notre Dame
- Project Mentor:
Swee Hong Chan
- Project Mentor Area:
Mathematics
- Project Abstract:
The 1/3−2/3 Conjecture states that in every finite partially ordered set that is not totally ordered, there exists a pair of elements x and y with the property that at least 1/3 and at most 2/3 of the linear extensions of the partial order place x earlier than y. This conjecture has become one of the more prominent conjectures in set theory, and while no one has succeeded to prove such a result for all partially ordered sets, there are partial results for posets with certain properties. Our goal this summer was to prove that this conjecture holds for a specific set P3,n. which consists of {x1, y1, z1, x2, y2, z2, ..., xn, yn, zn} where xi≤xi+1, yi≤yi+1, zi≤zi+1, and xi≤yi≤zi, for all i.
