4 papers
Proof of the Kahn Saks Conjecture
Max Aires
Let be the probability that precedes in a uniformly random linear extension of an -element poset , and define the balancing coefficient to be $…
Breaking the Infinite Barrier in the -- Conjecture
Max Aires, Swee Hong Chan, Igor Pak +1
The balance constant is a poset parameter measuring how well random linear extensions can be split according to their relative order on two elements. We give an -impro…
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…
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…