8 papers
Descent sets of cyclic permutations in types B and D
Kevin Liu
Elizalde constructed a bijection from the cyclic permutations to the symmetric group satisfying $\operatorname{Des}(π)\cap \{1,2,\ldots,n-1\}=\operatorname…
Descents and flag major index on conjugacy classes of colored permutation groups without short cycles
Kevin Liu, Mei Yin
We consider the descent and flag major index statistics on the colored permutation groups, which are wreath products of the form …
Universal rooted phylogenetic tree shapes and universal tanglegrams
Ann Clifton, Eva Czabarka, Kevin Liu +4
We provide an lower bound and an upper bound for the smallest size of rooted binary trees (a.k.a. phylogenetic tree shapes), which are universal for rooted b…
Moments of Colored Permutation Statistics on Conjugacy Classes
Jesse Campion Loth, Michael Levet, Kevin Liu +2
In this paper, we consider the moments of statistics on conjugacy classes of the colored permutation groups . We first show that…
Sampling planar tanglegrams and pairs of disjoint triangulations
Alexander E. Black, Kevin Liu, Alex Mcdonough +4
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that th…
Permutation Statistics in Conjugacy Classes of the Symmetric Group
Jesse Campion Loth, Michael Levet, Kevin Liu +3
We introduce the notion of a weighted inversion statistic on the symmetric group, and examine its distribution on each conjugacy class. Our work generalizes the study of several co…
A characterization of graphs with at most four boundary vertices
Nick Chiem, William Dudarov, Chris Lee +2
Steinerberger defined a notion of boundary for a graph and established a corresponding isoperimetric inquality. Hence, "large" graphs have more boundary vertices. In this paper, we…
Characterizing Planar Tanglegram Layouts and Applications to Edge Insertion Problems
Kevin Liu
Tanglegrams are formed by taking two rooted binary trees and with the same number of leaves and uniquely matching each leaf in with a leaf in . They are usually repr…