6 papers
Cutoff profiles for colored top-m-to-random shuffles with growing block size
Ivan Z. Feng
We study the -colored top--to-random shuffle on when the block size grows with . Let be the number of labels never touched after $k_…
Explicit cutoff profiles for colored top--to-random shuffles
Ivan Z. Feng
We study -colored top--to-random on the wreath product , with fixed. Using the Nakano-Sadahiro-Sakurai basis elements , we obtain exact nested-se…
The dual Burnside process
Ivan Z. Feng
The Burnside process is a classical Markov chain for sampling uniformly from group orbits. We introduce the dual Burnside process, obtained by interchanging the roles of group elem…
Analysis of a twisted Bose-Einstein Markov chain with applications to sampling Catalan structures
Ivan Z. Feng, J. E. Paguyo
We analyze a twisted Bose-Einstein Markov chain on arising from the Diaconis-Zhong twisted Burnside process. We derive explicit formulas for the transition kernel and stati…
The Math Teaching Atlas: Trails, Anchors, and Compass in Action
Ivan Z. Feng
Mathematics is a mountain, but students need more than descriptions of the view: they need a trail they can actually walk. This paper presents the Math Teaching Atlas, a framework…
Periodicity Uncovered: A Deep Dive into Bott's Theorems in K-Theory and Fiber Bundles
Ivan Z. Feng
This paper presents a comparison between two versions of Bott Periodicity Theorems: one in topological K-theory and the other in stable homotopy groups of classical groups. It begi…