2 papers
math.CO2025
Variance vs. range for linear extensions, and balancing extensions in posets of bounded width
Max Aires, Jeff Kahn
An old conjecture of Kahn and Saks says, roughly, that any poset of large enough width contains elements which are "balanced" in the sense that the probability that p…
math.CO2025
Balancing Extensions in Posets of Large Width
Max Aires, Jeff Kahn
We revisit classic balancing problems for linear extensions of a partially ordered set , proving results that go far beyond many of the best earlier results on this topic. For e…