6 citations · 13 across the 5 of their papers we have counts for
8 papers
Enumerative Theory for the Tsetlin Library
Sourav Chatterjee, Persi Diaconis, Gene B. Kim
The Tsetlin library is a well-studied Markov chain on the symmetric group . It has stationary distribution the Luce model, a nonuniform distribution on , which app…
On the joint distribution of descents and signs of permutations
Jason Fulman, Gene B. Kim, Sangchul Lee +1
We study the joint distribution of descents and sign for elements of the symmetric group and the hyperoctahedral group (Coxeter groups of types and ). For both groups, this…
The Absolute Orders on the Coxeter Groups and are Sperner
Lawrence H. Harper, Gene B. Kim, Neal Livesay
Over 50 years ago, Rota posted the following celebrated `Research Problem': prove or disprove that the partial order of partitions on an -set (i.e., the refinement order) is Spe…
Central limit theorem for peaks of a random permutation in a fixed conjugacy class of
Jason Fulman, Gene B. Kim, Sangchul Lee
The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a f…
Is the Symmetric Group Sperner?
Larry H. Harper, Gene B. Kim
An antichain in a poset is a subset of in which no two elements are comparable. Sperner showed that the maximal antichain in the Boolean l…
A central limit theorem for descents and major indices in fixed conjugacy classes of
Gene B. Kim, Sangchul Lee
The distribution of descents in fixed conjugacy classes of has been studied, and it is shown that its moments have interesting properties. Kim and Lee showed, by using Curtis…
Central limit theorem for descents in conjugacy classes of
Gene B. Kim, Sangchul Lee
The distribution of descents in fixed conjugacy classes of has been studied, and it is shown that its moments have interesting properties. Fulman proved that the descent numb…
Distribution of descents in matchings
Gene B. Kim
The distribution of descents in a fixed conjugacy class of is studied, and it is shown that its moments have an interesting property. A particular conjugacy class that is of…