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
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…
math.CO2023
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…