3 papers
math.PR2024
Cutoff for the Biased Random Transposition Shuffle
Evita Nestoridi, Alan Yan
In this paper, we study the biased random transposition shuffle, a natural generalization of the classical random transposition shuffle studied by Diaconis and Shahshahani. We diag…
math.CO2024
The extremals of the Kahn-Saks inequality
Ramon van Handel, Alan Yan, Xinmeng Zeng
A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distingui…
math.CO2024
Log-concavity in Combinatorics
Alan Yan
We survey some of the mechanisms used to prove that naturally defined sequences in combinatorics are log-concave. Among these mechanisms are Alexandrov's inequality for mixed discr…